x(x+2)=137

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Solution for x(x+2)=137 equation:


Simplifying
x(x + 2) = 137

Reorder the terms:
x(2 + x) = 137
(2 * x + x * x) = 137
(2x + x2) = 137

Solving
2x + x2 = 137

Solving for variable 'x'.

Reorder the terms:
-137 + 2x + x2 = 137 + -137

Combine like terms: 137 + -137 = 0
-137 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '137' to each side of the equation.
-137 + 2x + 137 + x2 = 0 + 137

Reorder the terms:
-137 + 137 + 2x + x2 = 0 + 137

Combine like terms: -137 + 137 = 0
0 + 2x + x2 = 0 + 137
2x + x2 = 0 + 137

Combine like terms: 0 + 137 = 137
2x + x2 = 137

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 = 137 + 1

Reorder the terms:
1 + 2x + x2 = 137 + 1

Combine like terms: 137 + 1 = 138
1 + 2x + x2 = 138

Factor a perfect square on the left side:
(x + 1)(x + 1) = 138

Calculate the square root of the right side: 11.747340124

Break this problem into two subproblems by setting 
(x + 1) equal to 11.747340124 and -11.747340124.

Subproblem 1

x + 1 = 11.747340124 Simplifying x + 1 = 11.747340124 Reorder the terms: 1 + x = 11.747340124 Solving 1 + x = 11.747340124 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 = 11.747340124 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.747340124 + -1 x = 11.747340124 + -1 Combine like terms: 11.747340124 + -1 = 10.747340124 x = 10.747340124 Simplifying x = 10.747340124

Subproblem 2

x + 1 = -11.747340124 Simplifying x + 1 = -11.747340124 Reorder the terms: 1 + x = -11.747340124 Solving 1 + x = -11.747340124 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 = -11.747340124 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.747340124 + -1 x = -11.747340124 + -1 Combine like terms: -11.747340124 + -1 = -12.747340124 x = -12.747340124 Simplifying x = -12.747340124

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.747340124, -12.747340124}

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