x^2-2=-8x

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Solution for x^2-2=-8x equation:


Simplifying
x2 + -2 = -8x

Reorder the terms:
-2 + x2 = -8x

Solving
-2 + x2 = -8x

Solving for variable 'x'.

Reorder the terms:
-2 + 8x + x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-2 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 8x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 8x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 8x + x2 = 0 + 2
8x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
8x + x2 = 2

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 2 + 16

Reorder the terms:
16 + 8x + x2 = 2 + 16

Combine like terms: 2 + 16 = 18
16 + 8x + x2 = 18

Factor a perfect square on the left side:
(x + 4)(x + 4) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + 4) equal to 4.242640687 and -4.242640687.

Subproblem 1

x + 4 = 4.242640687 Simplifying x + 4 = 4.242640687 Reorder the terms: 4 + x = 4.242640687 Solving 4 + x = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.242640687 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.242640687 + -4 x = 4.242640687 + -4 Combine like terms: 4.242640687 + -4 = 0.242640687 x = 0.242640687 Simplifying x = 0.242640687

Subproblem 2

x + 4 = -4.242640687 Simplifying x + 4 = -4.242640687 Reorder the terms: 4 + x = -4.242640687 Solving 4 + x = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.242640687 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.242640687 + -4 x = -4.242640687 + -4 Combine like terms: -4.242640687 + -4 = -8.242640687 x = -8.242640687 Simplifying x = -8.242640687

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.242640687, -8.242640687}

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