6x^2+80x-450=0

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Solution for 6x^2+80x-450=0 equation: 


Simplifying
6x2 + 80x + -450 = 0

Reorder the terms:
-450 + 80x + 6x2 = 0

Solving
-450 + 80x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-225 + 40x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-225 + 40x + 3x2)' equal to zero and attempt to solve:

Simplifying
-225 + 40x + 3x2 = 0

Solving
-225 + 40x + 3x2 = 0

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

Divide each side by '3'.
-75 + 13.33333333x + x2 = 0

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 13.33333333x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + 13.33333333x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 13.33333333x + x2 = 0 + 75
13.33333333x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
13.33333333x + x2 = 75

The x term is 13.33333333x.  Take half its coefficient (6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
13.33333333x + 44.44444442 + x2 = 75 + 44.44444442

Reorder the terms:
44.44444442 + 13.33333333x + x2 = 75 + 44.44444442

Combine like terms: 75 + 44.44444442 = 119.44444442
44.44444442 + 13.33333333x + x2 = 119.44444442

Factor a perfect square on the left side:
(x + 6.666666665)(x + 6.666666665) = 119.44444442

Calculate the square root of the right side: 10.929064206

Break this problem into two subproblems by setting 
(x + 6.666666665) equal to 10.929064206 and -10.929064206.


Subproblem 1
x + 6.666666665 = 10.929064206

Simplifying
x + 6.666666665 = 10.929064206

Reorder the terms:
6.666666665 + x = 10.929064206

Solving
6.666666665 + x = 10.929064206

Solving for variable 'x'.

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

Add '-6.666666665' to each side of the equation.
6.666666665 + -6.666666665 + x = 10.929064206 + -6.666666665

Combine like terms: 6.666666665 + -6.666666665 = 0.000000000
0.000000000 + x = 10.929064206 + -6.666666665
x = 10.929064206 + -6.666666665

Combine like terms: 10.929064206 + -6.666666665 = 4.262397541
x = 4.262397541

Simplifying
x = 4.262397541


Subproblem 2
x + 6.666666665 = -10.929064206

Simplifying
x + 6.666666665 = -10.929064206

Reorder the terms:
6.666666665 + x = -10.929064206

Solving
6.666666665 + x = -10.929064206

Solving for variable 'x'.

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

Add '-6.666666665' to each side of the equation.
6.666666665 + -6.666666665 + x = -10.929064206 + -6.666666665

Combine like terms: 6.666666665 + -6.666666665 = 0.000000000
0.000000000 + x = -10.929064206 + -6.666666665
x = -10.929064206 + -6.666666665

Combine like terms: -10.929064206 + -6.666666665 = -17.595730871
x = -17.595730871

Simplifying
x = -17.595730871


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.262397541, -17.595730871}
Solution
x = {4.262397541, -17.595730871}

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