x^2-2x-147=0

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Solution for x^2-2x-147=0 equation:


Simplifying
x2 + -2x + -147 = 0

Reorder the terms:
-147 + -2x + x2 = 0

Solving
-147 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '147' to each side of the equation.
-147 + -2x + 147 + x2 = 0 + 147

Reorder the terms:
-147 + 147 + -2x + x2 = 0 + 147

Combine like terms: -147 + 147 = 0
0 + -2x + x2 = 0 + 147
-2x + x2 = 0 + 147

Combine like terms: 0 + 147 = 147
-2x + x2 = 147

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 = 147 + 1

Reorder the terms:
1 + -2x + x2 = 147 + 1

Combine like terms: 147 + 1 = 148
1 + -2x + x2 = 148

Factor a perfect square on the left side:
(x + -1)(x + -1) = 148

Calculate the square root of the right side: 12.165525061

Break this problem into two subproblems by setting 
(x + -1) equal to 12.165525061 and -12.165525061.

Subproblem 1

x + -1 = 12.165525061 Simplifying x + -1 = 12.165525061 Reorder the terms: -1 + x = 12.165525061 Solving -1 + x = 12.165525061 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 = 12.165525061 + 1 Combine like terms: -1 + 1 = 0 0 + x = 12.165525061 + 1 x = 12.165525061 + 1 Combine like terms: 12.165525061 + 1 = 13.165525061 x = 13.165525061 Simplifying x = 13.165525061

Subproblem 2

x + -1 = -12.165525061 Simplifying x + -1 = -12.165525061 Reorder the terms: -1 + x = -12.165525061 Solving -1 + x = -12.165525061 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 = -12.165525061 + 1 Combine like terms: -1 + 1 = 0 0 + x = -12.165525061 + 1 x = -12.165525061 + 1 Combine like terms: -12.165525061 + 1 = -11.165525061 x = -11.165525061 Simplifying x = -11.165525061

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.165525061, -11.165525061}

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