Solve x2 64

Solve x2 64 DEFAULT
Hint: First of all, find the common factor of the given quadratic equation in the question. After finding the common factor apply zero product property and set each variable factor equal to zero.

Complete step by step solution:
We have been given that we have to find the value of x, ${x^2} = 64$. So first we will move all the terms to one side of the equation, usually the left, using the addition and subtraction property.
Then factoring the given quadratic equation according to the given expression and then apply the zero product property and set each variable factor equal to zero. So, the given quadratic equation is,
$ \Rightarrow {x^2} = 64$
From the above expression, we have to move the all the terms to one side of the equation usually the left side,
$ \Rightarrow {x^2} - 64 = 0$
After moving all the terms of the equation we get –
$ \Rightarrow {x^2} - 64 = 0$
 Doing further operations to solve the quadratic polynomial that we usually do,
$ \Rightarrow {x^2} + 8x - 8x + 64 = 0$
Then take the common from this equation, we get –
$ \Rightarrow x\left( {x + 8} \right) - 8\left( {x + 8} \right) = 0$
Now, we have two factors (x+8) and (x-8).
 $ \Rightarrow \left( {x + 8} \right)\left( {x - 8} \right) = 0$
Then, we will set each factor equal to zero and we get –
Two subproblems:
$ \Rightarrow \left( {x + 8} \right) = 0$
$ \Rightarrow $$\left( {x - 8} \right) = 0$
Solving the first subproblems, we get –
$ \Rightarrow $$\left( {x + 8} \right) = 0$, gives $x = - 8$
Again, solving the second subproblems, we get –
$ \Rightarrow $$\left( {x - 8} \right) = 0$, gives $x = 8$
                 Or
$ \Rightarrow $$x = \pm 8$

Hence, the required answer is, $ \pm 8$

Note:
We can also solve this question by the alternative method: Taking the square root of both sides of this equation. When we do the square root of any number, we get two values one the positive and another negative value.
Sours: https://www.vedantu.com/question-answer/how-do-you-solve-x2-64-class-8-maths-cbse-5ff948b2bfdd3912f3aac407

Nonlinear equations

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                     x^2-(-64)=0 

Step by step solution :

Step  1  :

Polynomial Roots Calculator :

 1.1    Find roots (zeroes) of :       F(x) = x2+64
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  64.

 The factor(s) are:

of the Leading Coefficient :  1
 of the Trailing Constant :  1 ,2 ,4 ,8 ,16 ,32 ,64

 Let us test ....

  P  Q  P/Q  F(P/Q)   Divisor
     -1     1      -1.00      65.00   
     -2     1      -2.00      68.00   
     -4     1      -4.00      80.00   
     -8     1      -8.00      128.00   
     -16     1     -16.00      320.00   
     -32     1     -32.00      1088.00   
     -64     1     -64.00      4160.00   
     1     1      1.00      65.00   
     2     1      2.00      68.00   
     4     1      4.00      80.00   
     8     1      8.00      128.00   
     16     1      16.00      320.00   
     32     1      32.00      1088.00   
     64     1      64.00      4160.00   


Polynomial Roots Calculator found no rational roots

Equation at the end of step  1  :

x2 + 64 = 0

Step  2  :

Solving a Single Variable Equation :

 2.1      Solve  :    x2+64 = 0 

 Subtract  64  from both sides of the equation : 
                      x2 = -64
 
 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  
                      x  =  ± √ -64  

 In Math,  i  is called the imaginary unit. It satisfies   i2  =-1. Both   i   and   -i   are the square roots of   -1 

Accordingly,  √ -64  =
                    √ -1• 64   =
                    √ -1 •√ 64   =
                    i •  √ 64

Can  √ 64 be simplified ?

Yes!   The prime factorization of  64   is
   2•2•2•2•2•2 
To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 64   =  √ 2•2•2•2•2•2  =2•2•2•√ 1   =
                ±  8 • √ 1   =
                ±  8

The equation has no real solutions. It has 2 imaginary, or complex solutions.

                      x=  0.0000 + 8.0000 i 
                      x=  0.0000 - 8.0000 i 

Two solutions were found :

  1.   x=  0.0000 - 8.0000 i 
  2.   x=  0.0000 + 8.0000 i 
Sours: https://www.tiger-algebra.com/drill/x~2=-64/
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Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2". 

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                     x^2-(64)=0 

Step by step solution :

Step  1  :

Trying to factor as a Difference of Squares :

 1.1      Factoring:  x2-64 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2- AB + AB - B2 =
         A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 64 is the square of 8
Check :  x2  is the square of  x1 

Factorization is :       (x + 8)  •  (x - 8) 

Equation at the end of step  1  :

(x + 8) • (x - 8) = 0

Step  2  :

Theory - Roots of a product :

 2.1    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

 2.2      Solve  :    x+8 = 0 

 Subtract  8  from both sides of the equation : 
                      x = -8

Solving a Single Variable Equation :

 2.3      Solve  :    x-8 = 0 

 Add  8  to both sides of the equation : 
                      x = 8

Two solutions were found :

  1.  x = 8
  2.  x = -8
Sours: https://www.tiger-algebra.com/drill/x2=64/
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Solution for x2=64, equation:



x2=64.
We move all terms to the left:
x2-(64.)=0
We add all the numbers together, and all the variables
x2-64=0
We add all the numbers together, and all the variables
x^2-64=0
a = 1; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·1·(-64)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$

$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$


$\sqrt{\Delta}=\sqrt{256}=16$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*1}=\frac{-16}{2} =-8 $

$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*1}=\frac{16}{2} =8 $

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Sours: https://www.geteasysolution.com/x2=64,

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