6x^2-40x-525=0

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Solution for 6x^2-40x-525=0 equation: 


Simplifying
6x2 + -40x + -525 = 0

Reorder the terms:
-525 + -40x + 6x2 = 0

Solving
-525 + -40x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-87.5 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '87.5' to each side of the equation.
-87.5 + -6.666666667x + 87.5 + x2 = 0 + 87.5

Reorder the terms:
-87.5 + 87.5 + -6.666666667x + x2 = 0 + 87.5

Combine like terms: -87.5 + 87.5 = 0.0
0.0 + -6.666666667x + x2 = 0 + 87.5
-6.666666667x + x2 = 0 + 87.5

Combine like terms: 0 + 87.5 = 87.5
-6.666666667x + x2 = 87.5

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = 87.5 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = 87.5 + 11.11111112

Combine like terms: 87.5 + 11.11111112 = 98.61111112
11.11111112 + -6.666666667x + x2 = 98.61111112

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 98.61111112

Calculate the square root of the right side: 9.93031274

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 9.93031274 and -9.93031274.


Subproblem 1
x + -3.333333334 = 9.93031274

Simplifying
x + -3.333333334 = 9.93031274

Reorder the terms:
-3.333333334 + x = 9.93031274

Solving
-3.333333334 + x = 9.93031274

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 9.93031274 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 9.93031274 + 3.333333334
x = 9.93031274 + 3.333333334

Combine like terms: 9.93031274 + 3.333333334 = 13.263646074
x = 13.263646074

Simplifying
x = 13.263646074


Subproblem 2
x + -3.333333334 = -9.93031274

Simplifying
x + -3.333333334 = -9.93031274

Reorder the terms:
-3.333333334 + x = -9.93031274

Solving
-3.333333334 + x = -9.93031274

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -9.93031274 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -9.93031274 + 3.333333334
x = -9.93031274 + 3.333333334

Combine like terms: -9.93031274 + 3.333333334 = -6.596979406
x = -6.596979406

Simplifying
x = -6.596979406


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.263646074, -6.596979406}

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