x^2+88x+125=0

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Solution for x^2+88x+125=0 equation:


Simplifying
x2 + 88x + 125 = 0

Reorder the terms:
125 + 88x + x2 = 0

Solving
125 + 88x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-125' to each side of the equation.
125 + 88x + -125 + x2 = 0 + -125

Reorder the terms:
125 + -125 + 88x + x2 = 0 + -125

Combine like terms: 125 + -125 = 0
0 + 88x + x2 = 0 + -125
88x + x2 = 0 + -125

Combine like terms: 0 + -125 = -125
88x + x2 = -125

The x term is 88x.  Take half its coefficient (44).
Square it (1936) and add it to both sides.

Add '1936' to each side of the equation.
88x + 1936 + x2 = -125 + 1936

Reorder the terms:
1936 + 88x + x2 = -125 + 1936

Combine like terms: -125 + 1936 = 1811
1936 + 88x + x2 = 1811

Factor a perfect square on the left side:
(x + 44)(x + 44) = 1811

Calculate the square root of the right side: 42.555845662

Break this problem into two subproblems by setting 
(x + 44) equal to 42.555845662 and -42.555845662.

Subproblem 1

x + 44 = 42.555845662 Simplifying x + 44 = 42.555845662 Reorder the terms: 44 + x = 42.555845662 Solving 44 + x = 42.555845662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-44' to each side of the equation. 44 + -44 + x = 42.555845662 + -44 Combine like terms: 44 + -44 = 0 0 + x = 42.555845662 + -44 x = 42.555845662 + -44 Combine like terms: 42.555845662 + -44 = -1.444154338 x = -1.444154338 Simplifying x = -1.444154338

Subproblem 2

x + 44 = -42.555845662 Simplifying x + 44 = -42.555845662 Reorder the terms: 44 + x = -42.555845662 Solving 44 + x = -42.555845662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-44' to each side of the equation. 44 + -44 + x = -42.555845662 + -44 Combine like terms: 44 + -44 = 0 0 + x = -42.555845662 + -44 x = -42.555845662 + -44 Combine like terms: -42.555845662 + -44 = -86.555845662 x = -86.555845662 Simplifying x = -86.555845662

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.444154338, -86.555845662}

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