x(x+2)=158

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Solution for x(x+2)=158 equation:


Simplifying
x(x + 2) = 158

Reorder the terms:
x(2 + x) = 158
(2 * x + x * x) = 158
(2x + x2) = 158

Solving
2x + x2 = 158

Solving for variable 'x'.

Reorder the terms:
-158 + 2x + x2 = 158 + -158

Combine like terms: 158 + -158 = 0
-158 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '158' to each side of the equation.
-158 + 2x + 158 + x2 = 0 + 158

Reorder the terms:
-158 + 158 + 2x + x2 = 0 + 158

Combine like terms: -158 + 158 = 0
0 + 2x + x2 = 0 + 158
2x + x2 = 0 + 158

Combine like terms: 0 + 158 = 158
2x + x2 = 158

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 = 158 + 1

Reorder the terms:
1 + 2x + x2 = 158 + 1

Combine like terms: 158 + 1 = 159
1 + 2x + x2 = 159

Factor a perfect square on the left side:
(x + 1)(x + 1) = 159

Calculate the square root of the right side: 12.609520213

Break this problem into two subproblems by setting 
(x + 1) equal to 12.609520213 and -12.609520213.

Subproblem 1

x + 1 = 12.609520213 Simplifying x + 1 = 12.609520213 Reorder the terms: 1 + x = 12.609520213 Solving 1 + x = 12.609520213 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 = 12.609520213 + -1 Combine like terms: 1 + -1 = 0 0 + x = 12.609520213 + -1 x = 12.609520213 + -1 Combine like terms: 12.609520213 + -1 = 11.609520213 x = 11.609520213 Simplifying x = 11.609520213

Subproblem 2

x + 1 = -12.609520213 Simplifying x + 1 = -12.609520213 Reorder the terms: 1 + x = -12.609520213 Solving 1 + x = -12.609520213 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 = -12.609520213 + -1 Combine like terms: 1 + -1 = 0 0 + x = -12.609520213 + -1 x = -12.609520213 + -1 Combine like terms: -12.609520213 + -1 = -13.609520213 x = -13.609520213 Simplifying x = -13.609520213

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.609520213, -13.609520213}

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