x^2+2x=220

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Solution for x^2+2x=220 equation:


Simplifying
x2 + 2x = 220

Reorder the terms:
2x + x2 = 220

Solving
2x + x2 = 220

Solving for variable 'x'.

Reorder the terms:
-220 + 2x + x2 = 220 + -220

Combine like terms: 220 + -220 = 0
-220 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '220' to each side of the equation.
-220 + 2x + 220 + x2 = 0 + 220

Reorder the terms:
-220 + 220 + 2x + x2 = 0 + 220

Combine like terms: -220 + 220 = 0
0 + 2x + x2 = 0 + 220
2x + x2 = 0 + 220

Combine like terms: 0 + 220 = 220
2x + x2 = 220

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 = 220 + 1

Reorder the terms:
1 + 2x + x2 = 220 + 1

Combine like terms: 220 + 1 = 221
1 + 2x + x2 = 221

Factor a perfect square on the left side:
(x + 1)(x + 1) = 221

Calculate the square root of the right side: 14.866068747

Break this problem into two subproblems by setting 
(x + 1) equal to 14.866068747 and -14.866068747.

Subproblem 1

x + 1 = 14.866068747 Simplifying x + 1 = 14.866068747 Reorder the terms: 1 + x = 14.866068747 Solving 1 + x = 14.866068747 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 = 14.866068747 + -1 Combine like terms: 1 + -1 = 0 0 + x = 14.866068747 + -1 x = 14.866068747 + -1 Combine like terms: 14.866068747 + -1 = 13.866068747 x = 13.866068747 Simplifying x = 13.866068747

Subproblem 2

x + 1 = -14.866068747 Simplifying x + 1 = -14.866068747 Reorder the terms: 1 + x = -14.866068747 Solving 1 + x = -14.866068747 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 = -14.866068747 + -1 Combine like terms: 1 + -1 = 0 0 + x = -14.866068747 + -1 x = -14.866068747 + -1 Combine like terms: -14.866068747 + -1 = -15.866068747 x = -15.866068747 Simplifying x = -15.866068747

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.866068747, -15.866068747}

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