x(x+2)=136

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Solution for x(x+2)=136 equation:


Simplifying
x(x + 2) = 136

Reorder the terms:
x(2 + x) = 136
(2 * x + x * x) = 136
(2x + x2) = 136

Solving
2x + x2 = 136

Solving for variable 'x'.

Reorder the terms:
-136 + 2x + x2 = 136 + -136

Combine like terms: 136 + -136 = 0
-136 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '136' to each side of the equation.
-136 + 2x + 136 + x2 = 0 + 136

Reorder the terms:
-136 + 136 + 2x + x2 = 0 + 136

Combine like terms: -136 + 136 = 0
0 + 2x + x2 = 0 + 136
2x + x2 = 0 + 136

Combine like terms: 0 + 136 = 136
2x + x2 = 136

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 = 136 + 1

Reorder the terms:
1 + 2x + x2 = 136 + 1

Combine like terms: 136 + 1 = 137
1 + 2x + x2 = 137

Factor a perfect square on the left side:
(x + 1)(x + 1) = 137

Calculate the square root of the right side: 11.704699911

Break this problem into two subproblems by setting 
(x + 1) equal to 11.704699911 and -11.704699911.

Subproblem 1

x + 1 = 11.704699911 Simplifying x + 1 = 11.704699911 Reorder the terms: 1 + x = 11.704699911 Solving 1 + x = 11.704699911 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 = 11.704699911 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.704699911 + -1 x = 11.704699911 + -1 Combine like terms: 11.704699911 + -1 = 10.704699911 x = 10.704699911 Simplifying x = 10.704699911

Subproblem 2

x + 1 = -11.704699911 Simplifying x + 1 = -11.704699911 Reorder the terms: 1 + x = -11.704699911 Solving 1 + x = -11.704699911 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 = -11.704699911 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.704699911 + -1 x = -11.704699911 + -1 Combine like terms: -11.704699911 + -1 = -12.704699911 x = -12.704699911 Simplifying x = -12.704699911

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.704699911, -12.704699911}

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