(x-4)(x-4)-147=0

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Solution for (x-4)(x-4)-147=0 equation:


Simplifying
(x + -4)(x + -4) + -147 = 0

Reorder the terms:
(-4 + x)(x + -4) + -147 = 0

Reorder the terms:
(-4 + x)(-4 + x) + -147 = 0

Multiply (-4 + x) * (-4 + x)
(-4(-4 + x) + x(-4 + x)) + -147 = 0
((-4 * -4 + x * -4) + x(-4 + x)) + -147 = 0
((16 + -4x) + x(-4 + x)) + -147 = 0
(16 + -4x + (-4 * x + x * x)) + -147 = 0
(16 + -4x + (-4x + x2)) + -147 = 0

Combine like terms: -4x + -4x = -8x
(16 + -8x + x2) + -147 = 0

Reorder the terms:
16 + -147 + -8x + x2 = 0

Combine like terms: 16 + -147 = -131
-131 + -8x + x2 = 0

Solving
-131 + -8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '131' to each side of the equation.
-131 + -8x + 131 + x2 = 0 + 131

Reorder the terms:
-131 + 131 + -8x + x2 = 0 + 131

Combine like terms: -131 + 131 = 0
0 + -8x + x2 = 0 + 131
-8x + x2 = 0 + 131

Combine like terms: 0 + 131 = 131
-8x + x2 = 131

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 = 131 + 16

Reorder the terms:
16 + -8x + x2 = 131 + 16

Combine like terms: 131 + 16 = 147
16 + -8x + x2 = 147

Factor a perfect square on the left side:
(x + -4)(x + -4) = 147

Calculate the square root of the right side: 12.124355653

Break this problem into two subproblems by setting 
(x + -4) equal to 12.124355653 and -12.124355653.

Subproblem 1

x + -4 = 12.124355653 Simplifying x + -4 = 12.124355653 Reorder the terms: -4 + x = 12.124355653 Solving -4 + x = 12.124355653 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 = 12.124355653 + 4 Combine like terms: -4 + 4 = 0 0 + x = 12.124355653 + 4 x = 12.124355653 + 4 Combine like terms: 12.124355653 + 4 = 16.124355653 x = 16.124355653 Simplifying x = 16.124355653

Subproblem 2

x + -4 = -12.124355653 Simplifying x + -4 = -12.124355653 Reorder the terms: -4 + x = -12.124355653 Solving -4 + x = -12.124355653 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 = -12.124355653 + 4 Combine like terms: -4 + 4 = 0 0 + x = -12.124355653 + 4 x = -12.124355653 + 4 Combine like terms: -12.124355653 + 4 = -8.124355653 x = -8.124355653 Simplifying x = -8.124355653

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.124355653, -8.124355653}

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