0.75x^2+20x-27=0

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Solution for 0.75x^2+20x-27=0 equation: 


Simplifying
0.75x2 + 20x + -27 = 0

Reorder the terms:
-27 + 20x + 0.75x2 = 0

Solving
-27 + 20x + 0.75x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.75 the coefficient of the squared term: 

Divide each side by '0.75'.
-36 + 26.66666667x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 26.66666667x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 26.66666667x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 26.66666667x + x2 = 0 + 36
26.66666667x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
26.66666667x + x2 = 36

The x term is 26.66666667x.  Take half its coefficient (13.33333334).
Square it (177.7777780) and add it to both sides.

Add '177.7777780' to each side of the equation.
26.66666667x + 177.7777780 + x2 = 36 + 177.7777780

Reorder the terms:
177.7777780 + 26.66666667x + x2 = 36 + 177.7777780

Combine like terms: 36 + 177.7777780 = 213.777778
177.7777780 + 26.66666667x + x2 = 213.777778

Factor a perfect square on the left side:
(x + 13.33333334)(x + 13.33333334) = 213.777778

Calculate the square root of the right side: 14.621141474

Break this problem into two subproblems by setting 
(x + 13.33333334) equal to 14.621141474 and -14.621141474.


Subproblem 1
x + 13.33333334 = 14.621141474

Simplifying
x + 13.33333334 = 14.621141474

Reorder the terms:
13.33333334 + x = 14.621141474

Solving
13.33333334 + x = 14.621141474

Solving for variable 'x'.

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

Add '-13.33333334' to each side of the equation.
13.33333334 + -13.33333334 + x = 14.621141474 + -13.33333334

Combine like terms: 13.33333334 + -13.33333334 = 0.00000000
0.00000000 + x = 14.621141474 + -13.33333334
x = 14.621141474 + -13.33333334

Combine like terms: 14.621141474 + -13.33333334 = 1.287808134
x = 1.287808134

Simplifying
x = 1.287808134


Subproblem 2
x + 13.33333334 = -14.621141474

Simplifying
x + 13.33333334 = -14.621141474

Reorder the terms:
13.33333334 + x = -14.621141474

Solving
13.33333334 + x = -14.621141474

Solving for variable 'x'.

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

Add '-13.33333334' to each side of the equation.
13.33333334 + -13.33333334 + x = -14.621141474 + -13.33333334

Combine like terms: 13.33333334 + -13.33333334 = 0.00000000
0.00000000 + x = -14.621141474 + -13.33333334
x = -14.621141474 + -13.33333334

Combine like terms: -14.621141474 + -13.33333334 = -27.954474814
x = -27.954474814

Simplifying
x = -27.954474814


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.287808134, -27.954474814}

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