(x)(x+2)=130

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Solution for (x)(x+2)=130 equation:


Simplifying
(x)(x + 2) = 130

Reorder the terms:
x(2 + x) = 130
(2 * x + x * x) = 130
(2x + x2) = 130

Solving
2x + x2 = 130

Solving for variable 'x'.

Reorder the terms:
-130 + 2x + x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-130 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '130' to each side of the equation.
-130 + 2x + 130 + x2 = 0 + 130

Reorder the terms:
-130 + 130 + 2x + x2 = 0 + 130

Combine like terms: -130 + 130 = 0
0 + 2x + x2 = 0 + 130
2x + x2 = 0 + 130

Combine like terms: 0 + 130 = 130
2x + x2 = 130

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 = 130 + 1

Reorder the terms:
1 + 2x + x2 = 130 + 1

Combine like terms: 130 + 1 = 131
1 + 2x + x2 = 131

Factor a perfect square on the left side:
(x + 1)(x + 1) = 131

Calculate the square root of the right side: 11.445523142

Break this problem into two subproblems by setting 
(x + 1) equal to 11.445523142 and -11.445523142.

Subproblem 1

x + 1 = 11.445523142 Simplifying x + 1 = 11.445523142 Reorder the terms: 1 + x = 11.445523142 Solving 1 + x = 11.445523142 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 = 11.445523142 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.445523142 + -1 x = 11.445523142 + -1 Combine like terms: 11.445523142 + -1 = 10.445523142 x = 10.445523142 Simplifying x = 10.445523142

Subproblem 2

x + 1 = -11.445523142 Simplifying x + 1 = -11.445523142 Reorder the terms: 1 + x = -11.445523142 Solving 1 + x = -11.445523142 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 = -11.445523142 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.445523142 + -1 x = -11.445523142 + -1 Combine like terms: -11.445523142 + -1 = -12.445523142 x = -12.445523142 Simplifying x = -12.445523142

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.445523142, -12.445523142}

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