(x-1)(x-1)=162

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Solution for (x-1)(x-1)=162 equation:


Simplifying
(x + -1)(x + -1) = 162

Reorder the terms:
(-1 + x)(x + -1) = 162

Reorder the terms:
(-1 + x)(-1 + x) = 162

Multiply (-1 + x) * (-1 + x)
(-1(-1 + x) + x(-1 + x)) = 162
((-1 * -1 + x * -1) + x(-1 + x)) = 162
((1 + -1x) + x(-1 + x)) = 162
(1 + -1x + (-1 * x + x * x)) = 162
(1 + -1x + (-1x + x2)) = 162

Combine like terms: -1x + -1x = -2x
(1 + -2x + x2) = 162

Solving
1 + -2x + x2 = 162

Solving for variable 'x'.

Reorder the terms:
1 + -162 + -2x + x2 = 162 + -162

Combine like terms: 1 + -162 = -161
-161 + -2x + x2 = 162 + -162

Combine like terms: 162 + -162 = 0
-161 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '161' to each side of the equation.
-161 + -2x + 161 + x2 = 0 + 161

Reorder the terms:
-161 + 161 + -2x + x2 = 0 + 161

Combine like terms: -161 + 161 = 0
0 + -2x + x2 = 0 + 161
-2x + x2 = 0 + 161

Combine like terms: 0 + 161 = 161
-2x + x2 = 161

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 161 + 1

Reorder the terms:
1 + -2x + x2 = 161 + 1

Combine like terms: 161 + 1 = 162
1 + -2x + x2 = 162

Factor a perfect square on the left side:
(x + -1)(x + -1) = 162

Calculate the square root of the right side: 12.727922061

Break this problem into two subproblems by setting 
(x + -1) equal to 12.727922061 and -12.727922061.

Subproblem 1

x + -1 = 12.727922061 Simplifying x + -1 = 12.727922061 Reorder the terms: -1 + x = 12.727922061 Solving -1 + x = 12.727922061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 12.727922061 + 1 Combine like terms: -1 + 1 = 0 0 + x = 12.727922061 + 1 x = 12.727922061 + 1 Combine like terms: 12.727922061 + 1 = 13.727922061 x = 13.727922061 Simplifying x = 13.727922061

Subproblem 2

x + -1 = -12.727922061 Simplifying x + -1 = -12.727922061 Reorder the terms: -1 + x = -12.727922061 Solving -1 + x = -12.727922061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -12.727922061 + 1 Combine like terms: -1 + 1 = 0 0 + x = -12.727922061 + 1 x = -12.727922061 + 1 Combine like terms: -12.727922061 + 1 = -11.727922061 x = -11.727922061 Simplifying x = -11.727922061

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.727922061, -11.727922061}

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