x^2+26x+5=0

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Solution for x^2+26x+5=0 equation:


Simplifying
x2 + 26x + 5 = 0

Reorder the terms:
5 + 26x + x2 = 0

Solving
5 + 26x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 26x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 26x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 26x + x2 = 0 + -5
26x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
26x + x2 = -5

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 = -5 + 169

Reorder the terms:
169 + 26x + x2 = -5 + 169

Combine like terms: -5 + 169 = 164
169 + 26x + x2 = 164

Factor a perfect square on the left side:
(x + 13)(x + 13) = 164

Calculate the square root of the right side: 12.806248475

Break this problem into two subproblems by setting 
(x + 13) equal to 12.806248475 and -12.806248475.

Subproblem 1

x + 13 = 12.806248475 Simplifying x + 13 = 12.806248475 Reorder the terms: 13 + x = 12.806248475 Solving 13 + x = 12.806248475 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 = 12.806248475 + -13 Combine like terms: 13 + -13 = 0 0 + x = 12.806248475 + -13 x = 12.806248475 + -13 Combine like terms: 12.806248475 + -13 = -0.193751525 x = -0.193751525 Simplifying x = -0.193751525

Subproblem 2

x + 13 = -12.806248475 Simplifying x + 13 = -12.806248475 Reorder the terms: 13 + x = -12.806248475 Solving 13 + x = -12.806248475 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 = -12.806248475 + -13 Combine like terms: 13 + -13 = 0 0 + x = -12.806248475 + -13 x = -12.806248475 + -13 Combine like terms: -12.806248475 + -13 = -25.806248475 x = -25.806248475 Simplifying x = -25.806248475

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.193751525, -25.806248475}

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