x^2+2x=225

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Solution for x^2+2x=225 equation:


Simplifying
x2 + 2x = 225

Reorder the terms:
2x + x2 = 225

Solving
2x + x2 = 225

Solving for variable 'x'.

Reorder the terms:
-225 + 2x + x2 = 225 + -225

Combine like terms: 225 + -225 = 0
-225 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + 2x + 225 + x2 = 0 + 225

Reorder the terms:
-225 + 225 + 2x + x2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + 2x + x2 = 0 + 225
2x + x2 = 0 + 225

Combine like terms: 0 + 225 = 225
2x + x2 = 225

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 = 225 + 1

Reorder the terms:
1 + 2x + x2 = 225 + 1

Combine like terms: 225 + 1 = 226
1 + 2x + x2 = 226

Factor a perfect square on the left side:
(x + 1)(x + 1) = 226

Calculate the square root of the right side: 15.033296378

Break this problem into two subproblems by setting 
(x + 1) equal to 15.033296378 and -15.033296378.

Subproblem 1

x + 1 = 15.033296378 Simplifying x + 1 = 15.033296378 Reorder the terms: 1 + x = 15.033296378 Solving 1 + x = 15.033296378 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 = 15.033296378 + -1 Combine like terms: 1 + -1 = 0 0 + x = 15.033296378 + -1 x = 15.033296378 + -1 Combine like terms: 15.033296378 + -1 = 14.033296378 x = 14.033296378 Simplifying x = 14.033296378

Subproblem 2

x + 1 = -15.033296378 Simplifying x + 1 = -15.033296378 Reorder the terms: 1 + x = -15.033296378 Solving 1 + x = -15.033296378 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 = -15.033296378 + -1 Combine like terms: 1 + -1 = 0 0 + x = -15.033296378 + -1 x = -15.033296378 + -1 Combine like terms: -15.033296378 + -1 = -16.033296378 x = -16.033296378 Simplifying x = -16.033296378

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.033296378, -16.033296378}

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