x^2+2x-88=0

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Solution for x^2+2x-88=0 equation:


Simplifying
x2 + 2x + -88 = 0

Reorder the terms:
-88 + 2x + x2 = 0

Solving
-88 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '88' to each side of the equation.
-88 + 2x + 88 + x2 = 0 + 88

Reorder the terms:
-88 + 88 + 2x + x2 = 0 + 88

Combine like terms: -88 + 88 = 0
0 + 2x + x2 = 0 + 88
2x + x2 = 0 + 88

Combine like terms: 0 + 88 = 88
2x + x2 = 88

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 = 88 + 1

Reorder the terms:
1 + 2x + x2 = 88 + 1

Combine like terms: 88 + 1 = 89
1 + 2x + x2 = 89

Factor a perfect square on the left side:
(x + 1)(x + 1) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(x + 1) equal to 9.433981132 and -9.433981132.

Subproblem 1

x + 1 = 9.433981132 Simplifying x + 1 = 9.433981132 Reorder the terms: 1 + x = 9.433981132 Solving 1 + x = 9.433981132 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 = 9.433981132 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.433981132 + -1 x = 9.433981132 + -1 Combine like terms: 9.433981132 + -1 = 8.433981132 x = 8.433981132 Simplifying x = 8.433981132

Subproblem 2

x + 1 = -9.433981132 Simplifying x + 1 = -9.433981132 Reorder the terms: 1 + x = -9.433981132 Solving 1 + x = -9.433981132 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 = -9.433981132 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.433981132 + -1 x = -9.433981132 + -1 Combine like terms: -9.433981132 + -1 = -10.433981132 x = -10.433981132 Simplifying x = -10.433981132

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.433981132, -10.433981132}

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