(x-2)(x-2)=23

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Solution for (x-2)(x-2)=23 equation:


Simplifying
(x + -2)(x + -2) = 23

Reorder the terms:
(-2 + x)(x + -2) = 23

Reorder the terms:
(-2 + x)(-2 + x) = 23

Multiply (-2 + x) * (-2 + x)
(-2(-2 + x) + x(-2 + x)) = 23
((-2 * -2 + x * -2) + x(-2 + x)) = 23
((4 + -2x) + x(-2 + x)) = 23
(4 + -2x + (-2 * x + x * x)) = 23
(4 + -2x + (-2x + x2)) = 23

Combine like terms: -2x + -2x = -4x
(4 + -4x + x2) = 23

Solving
4 + -4x + x2 = 23

Solving for variable 'x'.

Reorder the terms:
4 + -23 + -4x + x2 = 23 + -23

Combine like terms: 4 + -23 = -19
-19 + -4x + x2 = 23 + -23

Combine like terms: 23 + -23 = 0
-19 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + -4x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + -4x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -4x + x2 = 0 + 19
-4x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
-4x + x2 = 19

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 = 19 + 4

Reorder the terms:
4 + -4x + x2 = 19 + 4

Combine like terms: 19 + 4 = 23
4 + -4x + x2 = 23

Factor a perfect square on the left side:
(x + -2)(x + -2) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(x + -2) equal to 4.795831523 and -4.795831523.

Subproblem 1

x + -2 = 4.795831523 Simplifying x + -2 = 4.795831523 Reorder the terms: -2 + x = 4.795831523 Solving -2 + x = 4.795831523 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 = 4.795831523 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.795831523 + 2 x = 4.795831523 + 2 Combine like terms: 4.795831523 + 2 = 6.795831523 x = 6.795831523 Simplifying x = 6.795831523

Subproblem 2

x + -2 = -4.795831523 Simplifying x + -2 = -4.795831523 Reorder the terms: -2 + x = -4.795831523 Solving -2 + x = -4.795831523 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 = -4.795831523 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.795831523 + 2 x = -4.795831523 + 2 Combine like terms: -4.795831523 + 2 = -2.795831523 x = -2.795831523 Simplifying x = -2.795831523

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.795831523, -2.795831523}

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