(x-2)(x-2)=8

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Solution for (x-2)(x-2)=8 equation:


Simplifying
(x + -2)(x + -2) = 8

Reorder the terms:
(-2 + x)(x + -2) = 8

Reorder the terms:
(-2 + x)(-2 + x) = 8

Multiply (-2 + x) * (-2 + x)
(-2(-2 + x) + x(-2 + x)) = 8
((-2 * -2 + x * -2) + x(-2 + x)) = 8
((4 + -2x) + x(-2 + x)) = 8
(4 + -2x + (-2 * x + x * x)) = 8
(4 + -2x + (-2x + x2)) = 8

Combine like terms: -2x + -2x = -4x
(4 + -4x + x2) = 8

Solving
4 + -4x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
4 + -8 + -4x + x2 = 8 + -8

Combine like terms: 4 + -8 = -4
-4 + -4x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-4 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -4x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -4x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -4x + x2 = 0 + 4
-4x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-4x + x2 = 4

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 4 + 4

Reorder the terms:
4 + -4x + x2 = 4 + 4

Combine like terms: 4 + 4 = 8
4 + -4x + x2 = 8

Factor a perfect square on the left side:
(x + -2)(x + -2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -2) equal to 2.828427125 and -2.828427125.

Subproblem 1

x + -2 = 2.828427125 Simplifying x + -2 = 2.828427125 Reorder the terms: -2 + x = 2.828427125 Solving -2 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.828427125 + 2 x = 2.828427125 + 2 Combine like terms: 2.828427125 + 2 = 4.828427125 x = 4.828427125 Simplifying x = 4.828427125

Subproblem 2

x + -2 = -2.828427125 Simplifying x + -2 = -2.828427125 Reorder the terms: -2 + x = -2.828427125 Solving -2 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.828427125 + 2 x = -2.828427125 + 2 Combine like terms: -2.828427125 + 2 = -0.828427125 x = -0.828427125 Simplifying x = -0.828427125

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.828427125, -0.828427125}

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