x^2-2x-1=144

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Solution for x^2-2x-1=144 equation:


Simplifying
x2 + -2x + -1 = 144

Reorder the terms:
-1 + -2x + x2 = 144

Solving
-1 + -2x + x2 = 144

Solving for variable 'x'.

Reorder the terms:
-1 + -144 + -2x + x2 = 144 + -144

Combine like terms: -1 + -144 = -145
-145 + -2x + x2 = 144 + -144

Combine like terms: 144 + -144 = 0
-145 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '145' to each side of the equation.
-145 + -2x + 145 + x2 = 0 + 145

Reorder the terms:
-145 + 145 + -2x + x2 = 0 + 145

Combine like terms: -145 + 145 = 0
0 + -2x + x2 = 0 + 145
-2x + x2 = 0 + 145

Combine like terms: 0 + 145 = 145
-2x + x2 = 145

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 = 145 + 1

Reorder the terms:
1 + -2x + x2 = 145 + 1

Combine like terms: 145 + 1 = 146
1 + -2x + x2 = 146

Factor a perfect square on the left side:
(x + -1)(x + -1) = 146

Calculate the square root of the right side: 12.083045974

Break this problem into two subproblems by setting 
(x + -1) equal to 12.083045974 and -12.083045974.

Subproblem 1

x + -1 = 12.083045974 Simplifying x + -1 = 12.083045974 Reorder the terms: -1 + x = 12.083045974 Solving -1 + x = 12.083045974 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 = 12.083045974 + 1 Combine like terms: -1 + 1 = 0 0 + x = 12.083045974 + 1 x = 12.083045974 + 1 Combine like terms: 12.083045974 + 1 = 13.083045974 x = 13.083045974 Simplifying x = 13.083045974

Subproblem 2

x + -1 = -12.083045974 Simplifying x + -1 = -12.083045974 Reorder the terms: -1 + x = -12.083045974 Solving -1 + x = -12.083045974 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 = -12.083045974 + 1 Combine like terms: -1 + 1 = 0 0 + x = -12.083045974 + 1 x = -12.083045974 + 1 Combine like terms: -12.083045974 + 1 = -11.083045974 x = -11.083045974 Simplifying x = -11.083045974

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.083045974, -11.083045974}

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