3x^2+20x-525=0

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Solution for 3x^2+20x-525=0 equation: 


Simplifying
3x2 + 20x + -525 = 0

Reorder the terms:
-525 + 20x + 3x2 = 0

Solving
-525 + 20x + 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'.
-175 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '175' to each side of the equation.
-175 + 6.666666667x + 175 + x2 = 0 + 175

Reorder the terms:
-175 + 175 + 6.666666667x + x2 = 0 + 175

Combine like terms: -175 + 175 = 0
0 + 6.666666667x + x2 = 0 + 175
6.666666667x + x2 = 0 + 175

Combine like terms: 0 + 175 = 175
6.666666667x + x2 = 175

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 = 175 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 175 + 11.11111112

Combine like terms: 175 + 11.11111112 = 186.11111112
11.11111112 + 6.666666667x + x2 = 186.11111112

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 186.11111112

Calculate the square root of the right side: 13.64225462

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 13.64225462 and -13.64225462.


Subproblem 1
x + 3.333333334 = 13.64225462

Simplifying
x + 3.333333334 = 13.64225462

Reorder the terms:
3.333333334 + x = 13.64225462

Solving
3.333333334 + x = 13.64225462

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 = 13.64225462 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 13.64225462 + -3.333333334
x = 13.64225462 + -3.333333334

Combine like terms: 13.64225462 + -3.333333334 = 10.308921286
x = 10.308921286

Simplifying
x = 10.308921286


Subproblem 2
x + 3.333333334 = -13.64225462

Simplifying
x + 3.333333334 = -13.64225462

Reorder the terms:
3.333333334 + x = -13.64225462

Solving
3.333333334 + x = -13.64225462

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 = -13.64225462 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -13.64225462 + -3.333333334
x = -13.64225462 + -3.333333334

Combine like terms: -13.64225462 + -3.333333334 = -16.975587954
x = -16.975587954

Simplifying
x = -16.975587954


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.308921286, -16.975587954}

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