x^2+15x+56.25=36.25

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Solution for x^2+15x+56.25=36.25 equation: 


Simplifying
x2 + 15x + 56.25 = 36.25

Reorder the terms:
56.25 + 15x + x2 = 36.25

Solving
56.25 + 15x + x2 = 36.25

Solving for variable 'x'.

Reorder the terms:
56.25 + -36.25 + 15x + x2 = 36.25 + -36.25

Combine like terms: 56.25 + -36.25 = 20
20 + 15x + x2 = 36.25 + -36.25

Combine like terms: 36.25 + -36.25 = 0.00
20 + 15x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + 15x + -20 + x2 = 0.00 + -20

Reorder the terms:
20 + -20 + 15x + x2 = 0.00 + -20

Combine like terms: 20 + -20 = 0
0 + 15x + x2 = 0.00 + -20
15x + x2 = 0.00 + -20

Combine like terms: 0.00 + -20 = -20
15x + x2 = -20

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -20 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -20 + 56.25

Combine like terms: -20 + 56.25 = 36.25
56.25 + 15x + x2 = 36.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(x + 7.5) equal to 6.020797289 and -6.020797289.


Subproblem 1
x + 7.5 = 6.020797289

Simplifying
x + 7.5 = 6.020797289

Reorder the terms:
7.5 + x = 6.020797289

Solving
7.5 + x = 6.020797289

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 6.020797289 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 6.020797289 + -7.5
x = 6.020797289 + -7.5

Combine like terms: 6.020797289 + -7.5 = -1.479202711
x = -1.479202711

Simplifying
x = -1.479202711


Subproblem 2
x + 7.5 = -6.020797289

Simplifying
x + 7.5 = -6.020797289

Reorder the terms:
7.5 + x = -6.020797289

Solving
7.5 + x = -6.020797289

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -6.020797289 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -6.020797289 + -7.5
x = -6.020797289 + -7.5

Combine like terms: -6.020797289 + -7.5 = -13.520797289
x = -13.520797289

Simplifying
x = -13.520797289


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.479202711, -13.520797289}

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