2.33x^2-15.15x-8.16=0

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Solution for 2.33x^2-15.15x-8.16=0 equation: 


Simplifying
2.33x2 + -15.15x + -8.16 = 0

Reorder the terms:
-8.16 + -15.15x + 2.33x2 = 0

Solving
-8.16 + -15.15x + 2.33x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.33'.
-3.502145923 + -6.502145923x + x2 = 0

Move the constant term to the right:

Add '3.502145923' to each side of the equation.
-3.502145923 + -6.502145923x + 3.502145923 + x2 = 0 + 3.502145923

Reorder the terms:
-3.502145923 + 3.502145923 + -6.502145923x + x2 = 0 + 3.502145923

Combine like terms: -3.502145923 + 3.502145923 = 0.000000000
0.000000000 + -6.502145923x + x2 = 0 + 3.502145923
-6.502145923x + x2 = 0 + 3.502145923

Combine like terms: 0 + 3.502145923 = 3.502145923
-6.502145923x + x2 = 3.502145923

The x term is -6.502145923x.  Take half its coefficient (-3.251072962).
Square it (10.56947540) and add it to both sides.

Add '10.56947540' to each side of the equation.
-6.502145923x + 10.56947540 + x2 = 3.502145923 + 10.56947540

Reorder the terms:
10.56947540 + -6.502145923x + x2 = 3.502145923 + 10.56947540

Combine like terms: 3.502145923 + 10.56947540 = 14.071621323
10.56947540 + -6.502145923x + x2 = 14.071621323

Factor a perfect square on the left side:
(x + -3.251072962)(x + -3.251072962) = 14.071621323

Calculate the square root of the right side: 3.751215979

Break this problem into two subproblems by setting 
(x + -3.251072962) equal to 3.751215979 and -3.751215979.


Subproblem 1
x + -3.251072962 = 3.751215979

Simplifying
x + -3.251072962 = 3.751215979

Reorder the terms:
-3.251072962 + x = 3.751215979

Solving
-3.251072962 + x = 3.751215979

Solving for variable 'x'.

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

Add '3.251072962' to each side of the equation.
-3.251072962 + 3.251072962 + x = 3.751215979 + 3.251072962

Combine like terms: -3.251072962 + 3.251072962 = 0.000000000
0.000000000 + x = 3.751215979 + 3.251072962
x = 3.751215979 + 3.251072962

Combine like terms: 3.751215979 + 3.251072962 = 7.002288941
x = 7.002288941

Simplifying
x = 7.002288941


Subproblem 2
x + -3.251072962 = -3.751215979

Simplifying
x + -3.251072962 = -3.751215979

Reorder the terms:
-3.251072962 + x = -3.751215979

Solving
-3.251072962 + x = -3.751215979

Solving for variable 'x'.

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

Add '3.251072962' to each side of the equation.
-3.251072962 + 3.251072962 + x = -3.751215979 + 3.251072962

Combine like terms: -3.251072962 + 3.251072962 = 0.000000000
0.000000000 + x = -3.751215979 + 3.251072962
x = -3.751215979 + 3.251072962

Combine like terms: -3.751215979 + 3.251072962 = -0.500143017
x = -0.500143017

Simplifying
x = -0.500143017


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.002288941, -0.500143017}

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