3x^2-40x-225=0

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Solution for 3x^2-40x-225=0 equation: 


Simplifying
3x2 + -40x + -225 = 0

Reorder the terms:
-225 + -40x + 3x2 = 0

Solving
-225 + -40x + 3x2 = 0

Solving for variable 'x'.

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 = 17.595730871
x = 17.595730871

Simplifying
x = 17.595730871


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 = -4.262397541
x = -4.262397541

Simplifying
x = -4.262397541


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

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