x^2+5x+6.24=0

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Solution for x^2+5x+6.24=0 equation: 


Simplifying
x2 + 5x + 6.24 = 0

Reorder the terms:
6.24 + 5x + x2 = 0

Solving
6.24 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-6.24' to each side of the equation.
6.24 + 5x + -6.24 + x2 = 0 + -6.24

Reorder the terms:
6.24 + -6.24 + 5x + x2 = 0 + -6.24

Combine like terms: 6.24 + -6.24 = 0.00
0.00 + 5x + x2 = 0 + -6.24
5x + x2 = 0 + -6.24

Combine like terms: 0 + -6.24 = -6.24
5x + x2 = -6.24

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -6.24 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -6.24 + 6.25

Combine like terms: -6.24 + 6.25 = 0.01
6.25 + 5x + x2 = 0.01

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 0.01

Calculate the square root of the right side: 0.1

Break this problem into two subproblems by setting 
(x + 2.5) equal to 0.1 and -0.1.


Subproblem 1
x + 2.5 = 0.1

Simplifying
x + 2.5 = 0.1

Reorder the terms:
2.5 + x = 0.1

Solving
2.5 + x = 0.1

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 0.1 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 0.1 + -2.5
x = 0.1 + -2.5

Combine like terms: 0.1 + -2.5 = -2.4
x = -2.4

Simplifying
x = -2.4


Subproblem 2
x + 2.5 = -0.1

Simplifying
x + 2.5 = -0.1

Reorder the terms:
2.5 + x = -0.1

Solving
2.5 + x = -0.1

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -0.1 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -0.1 + -2.5
x = -0.1 + -2.5

Combine like terms: -0.1 + -2.5 = -2.6
x = -2.6

Simplifying
x = -2.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.4, -2.6}

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