x^2+15x-28=0

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Solution for x^2+15x-28=0 equation: 


Simplifying
x2 + 15x + -28 = 0

Reorder the terms:
-28 + 15x + x2 = 0

Solving
-28 + 15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 15x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 15x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 15x + x2 = 0 + 28
15x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
15x + x2 = 28

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 = 28 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 28 + 56.25

Combine like terms: 28 + 56.25 = 84.25
56.25 + 15x + x2 = 84.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 84.25

Calculate the square root of the right side: 9.178779875

Break this problem into two subproblems by setting 
(x + 7.5) equal to 9.178779875 and -9.178779875.


Subproblem 1
x + 7.5 = 9.178779875

Simplifying
x + 7.5 = 9.178779875

Reorder the terms:
7.5 + x = 9.178779875

Solving
7.5 + x = 9.178779875

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 = 9.178779875 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 9.178779875 + -7.5
x = 9.178779875 + -7.5

Combine like terms: 9.178779875 + -7.5 = 1.678779875
x = 1.678779875

Simplifying
x = 1.678779875


Subproblem 2
x + 7.5 = -9.178779875

Simplifying
x + 7.5 = -9.178779875

Reorder the terms:
7.5 + x = -9.178779875

Solving
7.5 + x = -9.178779875

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 = -9.178779875 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -9.178779875 + -7.5
x = -9.178779875 + -7.5

Combine like terms: -9.178779875 + -7.5 = -16.678779875
x = -16.678779875

Simplifying
x = -16.678779875


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.678779875, -16.678779875}

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