x+64=x^2+2

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Solution for x+64=x^2+2 equation:


Simplifying
x + 64 = x2 + 2

Reorder the terms:
64 + x = x2 + 2

Reorder the terms:
64 + x = 2 + x2

Solving
64 + x = 2 + x2

Solving for variable 'x'.

Reorder the terms:
64 + -2 + x + -1x2 = 2 + x2 + -2 + -1x2

Combine like terms: 64 + -2 = 62
62 + x + -1x2 = 2 + x2 + -2 + -1x2

Reorder the terms:
62 + x + -1x2 = 2 + -2 + x2 + -1x2

Combine like terms: 2 + -2 = 0
62 + x + -1x2 = 0 + x2 + -1x2
62 + x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
62 + x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-62 + -1x + x2 = 0

Move the constant term to the right:

Add '62' to each side of the equation.
-62 + -1x + 62 + x2 = 0 + 62

Reorder the terms:
-62 + 62 + -1x + x2 = 0 + 62

Combine like terms: -62 + 62 = 0
0 + -1x + x2 = 0 + 62
-1x + x2 = 0 + 62

Combine like terms: 0 + 62 = 62
-1x + x2 = 62

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 62 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 62 + 0.25

Combine like terms: 62 + 0.25 = 62.25
0.25 + -1x + x2 = 62.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(x + 0.5) equal to 7.889866919 and -7.889866919.

Subproblem 1

x + 0.5 = 7.889866919 Simplifying x + 0.5 = 7.889866919 Reorder the terms: 0.5 + x = 7.889866919 Solving 0.5 + x = 7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 7.889866919 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.889866919 + -0.5 x = 7.889866919 + -0.5 Combine like terms: 7.889866919 + -0.5 = 7.389866919 x = 7.389866919 Simplifying x = 7.389866919

Subproblem 2

x + 0.5 = -7.889866919 Simplifying x + 0.5 = -7.889866919 Reorder the terms: 0.5 + x = -7.889866919 Solving 0.5 + x = -7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -7.889866919 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.889866919 + -0.5 x = -7.889866919 + -0.5 Combine like terms: -7.889866919 + -0.5 = -8.389866919 x = -8.389866919 Simplifying x = -8.389866919

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.389866919, -8.389866919}

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