x^2+25x+11=0

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Solution for x^2+25x+11=0 equation:


Simplifying
x2 + 25x + 11 = 0

Reorder the terms:
11 + 25x + x2 = 0

Solving
11 + 25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 25x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + 25x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 25x + x2 = 0 + -11
25x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
25x + x2 = -11

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = -11 + 156.25

Reorder the terms:
156.25 + 25x + x2 = -11 + 156.25

Combine like terms: -11 + 156.25 = 145.25
156.25 + 25x + x2 = 145.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 145.25

Calculate the square root of the right side: 12.051970793

Break this problem into two subproblems by setting 
(x + 12.5) equal to 12.051970793 and -12.051970793.

Subproblem 1

x + 12.5 = 12.051970793 Simplifying x + 12.5 = 12.051970793 Reorder the terms: 12.5 + x = 12.051970793 Solving 12.5 + x = 12.051970793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 12.051970793 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 12.051970793 + -12.5 x = 12.051970793 + -12.5 Combine like terms: 12.051970793 + -12.5 = -0.448029207 x = -0.448029207 Simplifying x = -0.448029207

Subproblem 2

x + 12.5 = -12.051970793 Simplifying x + 12.5 = -12.051970793 Reorder the terms: 12.5 + x = -12.051970793 Solving 12.5 + x = -12.051970793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -12.051970793 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -12.051970793 + -12.5 x = -12.051970793 + -12.5 Combine like terms: -12.051970793 + -12.5 = -24.551970793 x = -24.551970793 Simplifying x = -24.551970793

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.448029207, -24.551970793}

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