x^2+26x+66=0

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Solution for x^2+26x+66=0 equation: 


Simplifying
x2 + 26x + 66 = 0

Reorder the terms:
66 + 26x + x2 = 0

Solving
66 + 26x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-66' to each side of the equation.
66 + 26x + -66 + x2 = 0 + -66

Reorder the terms:
66 + -66 + 26x + x2 = 0 + -66

Combine like terms: 66 + -66 = 0
0 + 26x + x2 = 0 + -66
26x + x2 = 0 + -66

Combine like terms: 0 + -66 = -66
26x + x2 = -66

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 = -66 + 169

Reorder the terms:
169 + 26x + x2 = -66 + 169

Combine like terms: -66 + 169 = 103
169 + 26x + x2 = 103

Factor a perfect square on the left side:
(x + 13)(x + 13) = 103

Calculate the square root of the right side: 10.148891565

Break this problem into two subproblems by setting 
(x + 13) equal to 10.148891565 and -10.148891565.


Subproblem 1
x + 13 = 10.148891565

Simplifying
x + 13 = 10.148891565

Reorder the terms:
13 + x = 10.148891565

Solving
13 + x = 10.148891565

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 = 10.148891565 + -13

Combine like terms: 13 + -13 = 0
0 + x = 10.148891565 + -13
x = 10.148891565 + -13

Combine like terms: 10.148891565 + -13 = -2.851108435
x = -2.851108435

Simplifying
x = -2.851108435


Subproblem 2
x + 13 = -10.148891565

Simplifying
x + 13 = -10.148891565

Reorder the terms:
13 + x = -10.148891565

Solving
13 + x = -10.148891565

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 = -10.148891565 + -13

Combine like terms: 13 + -13 = 0
0 + x = -10.148891565 + -13
x = -10.148891565 + -13

Combine like terms: -10.148891565 + -13 = -23.148891565
x = -23.148891565

Simplifying
x = -23.148891565


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.851108435, -23.148891565}

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