x^2+18.75x-187.5=0

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Solution for x^2+18.75x-187.5=0 equation: 


Simplifying
x2 + 18.75x + -187.5 = 0

Reorder the terms:
-187.5 + 18.75x + x2 = 0

Solving
-187.5 + 18.75x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '187.5' to each side of the equation.
-187.5 + 18.75x + 187.5 + x2 = 0 + 187.5

Reorder the terms:
-187.5 + 187.5 + 18.75x + x2 = 0 + 187.5

Combine like terms: -187.5 + 187.5 = 0.0
0.0 + 18.75x + x2 = 0 + 187.5
18.75x + x2 = 0 + 187.5

Combine like terms: 0 + 187.5 = 187.5
18.75x + x2 = 187.5

The x term is 18.75x.  Take half its coefficient (9.375).
Square it (87.890625) and add it to both sides.

Add '87.890625' to each side of the equation.
18.75x + 87.890625 + x2 = 187.5 + 87.890625

Reorder the terms:
87.890625 + 18.75x + x2 = 187.5 + 87.890625

Combine like terms: 187.5 + 87.890625 = 275.390625
87.890625 + 18.75x + x2 = 275.390625

Factor a perfect square on the left side:
(x + 9.375)(x + 9.375) = 275.390625

Calculate the square root of the right side: 16.594897559

Break this problem into two subproblems by setting 
(x + 9.375) equal to 16.594897559 and -16.594897559.


Subproblem 1
x + 9.375 = 16.594897559

Simplifying
x + 9.375 = 16.594897559

Reorder the terms:
9.375 + x = 16.594897559

Solving
9.375 + x = 16.594897559

Solving for variable 'x'.

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

Add '-9.375' to each side of the equation.
9.375 + -9.375 + x = 16.594897559 + -9.375

Combine like terms: 9.375 + -9.375 = 0.000
0.000 + x = 16.594897559 + -9.375
x = 16.594897559 + -9.375

Combine like terms: 16.594897559 + -9.375 = 7.219897559
x = 7.219897559

Simplifying
x = 7.219897559


Subproblem 2
x + 9.375 = -16.594897559

Simplifying
x + 9.375 = -16.594897559

Reorder the terms:
9.375 + x = -16.594897559

Solving
9.375 + x = -16.594897559

Solving for variable 'x'.

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

Add '-9.375' to each side of the equation.
9.375 + -9.375 + x = -16.594897559 + -9.375

Combine like terms: 9.375 + -9.375 = 0.000
0.000 + x = -16.594897559 + -9.375
x = -16.594897559 + -9.375

Combine like terms: -16.594897559 + -9.375 = -25.969897559
x = -25.969897559

Simplifying
x = -25.969897559


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.219897559, -25.969897559}

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