x^2+26x+27=0

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Solution for x^2+26x+27=0 equation:


Simplifying
x2 + 26x + 27 = 0

Reorder the terms:
27 + 26x + x2 = 0

Solving
27 + 26x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + 26x + -27 + x2 = 0 + -27

Reorder the terms:
27 + -27 + 26x + x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 26x + x2 = 0 + -27
26x + x2 = 0 + -27

Combine like terms: 0 + -27 = -27
26x + x2 = -27

The x term is 26x.  Take half its coefficient (13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
26x + 169 + x2 = -27 + 169

Reorder the terms:
169 + 26x + x2 = -27 + 169

Combine like terms: -27 + 169 = 142
169 + 26x + x2 = 142

Factor a perfect square on the left side:
(x + 13)(x + 13) = 142

Calculate the square root of the right side: 11.916375288

Break this problem into two subproblems by setting 
(x + 13) equal to 11.916375288 and -11.916375288.

Subproblem 1

x + 13 = 11.916375288 Simplifying x + 13 = 11.916375288 Reorder the terms: 13 + x = 11.916375288 Solving 13 + x = 11.916375288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 11.916375288 + -13 Combine like terms: 13 + -13 = 0 0 + x = 11.916375288 + -13 x = 11.916375288 + -13 Combine like terms: 11.916375288 + -13 = -1.083624712 x = -1.083624712 Simplifying x = -1.083624712

Subproblem 2

x + 13 = -11.916375288 Simplifying x + 13 = -11.916375288 Reorder the terms: 13 + x = -11.916375288 Solving 13 + x = -11.916375288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -11.916375288 + -13 Combine like terms: 13 + -13 = 0 0 + x = -11.916375288 + -13 x = -11.916375288 + -13 Combine like terms: -11.916375288 + -13 = -24.916375288 x = -24.916375288 Simplifying x = -24.916375288

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.083624712, -24.916375288}

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