x^2=6-8x

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Solution for x^2=6-8x equation:


Simplifying
x2 = 6 + -8x

Solving
x2 = 6 + -8x

Solving for variable 'x'.

Reorder the terms:
-6 + 8x + x2 = 6 + -8x + -6 + 8x

Reorder the terms:
-6 + 8x + x2 = 6 + -6 + -8x + 8x

Combine like terms: 6 + -6 = 0
-6 + 8x + x2 = 0 + -8x + 8x
-6 + 8x + x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-6 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 8x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 8x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 8x + x2 = 0 + 6
8x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
8x + x2 = 6

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 = 6 + 16

Reorder the terms:
16 + 8x + x2 = 6 + 16

Combine like terms: 6 + 16 = 22
16 + 8x + x2 = 22

Factor a perfect square on the left side:
(x + 4)(x + 4) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(x + 4) equal to 4.69041576 and -4.69041576.

Subproblem 1

x + 4 = 4.69041576 Simplifying x + 4 = 4.69041576 Reorder the terms: 4 + x = 4.69041576 Solving 4 + x = 4.69041576 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 = 4.69041576 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.69041576 + -4 x = 4.69041576 + -4 Combine like terms: 4.69041576 + -4 = 0.69041576 x = 0.69041576 Simplifying x = 0.69041576

Subproblem 2

x + 4 = -4.69041576 Simplifying x + 4 = -4.69041576 Reorder the terms: 4 + x = -4.69041576 Solving 4 + x = -4.69041576 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 = -4.69041576 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.69041576 + -4 x = -4.69041576 + -4 Combine like terms: -4.69041576 + -4 = -8.69041576 x = -8.69041576 Simplifying x = -8.69041576

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.69041576, -8.69041576}

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