3x^2-90x-10=0

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Solution for 3x^2-90x-10=0 equation: 


Simplifying
3x2 + -90x + -10 = 0

Reorder the terms:
-10 + -90x + 3x2 = 0

Solving
-10 + -90x + 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'.
-3.333333333 + -30x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -30x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -30x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -30x + x2 = 0 + 3.333333333
-30x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-30x + x2 = 3.333333333

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = 3.333333333 + 225

Reorder the terms:
225 + -30x + x2 = 3.333333333 + 225

Combine like terms: 3.333333333 + 225 = 228.333333333
225 + -30x + x2 = 228.333333333

Factor a perfect square on the left side:
(x + -15)(x + -15) = 228.333333333

Calculate the square root of the right side: 15.110702609

Break this problem into two subproblems by setting 
(x + -15) equal to 15.110702609 and -15.110702609.


Subproblem 1
x + -15 = 15.110702609

Simplifying
x + -15 = 15.110702609

Reorder the terms:
-15 + x = 15.110702609

Solving
-15 + x = 15.110702609

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 15.110702609 + 15

Combine like terms: -15 + 15 = 0
0 + x = 15.110702609 + 15
x = 15.110702609 + 15

Combine like terms: 15.110702609 + 15 = 30.110702609
x = 30.110702609

Simplifying
x = 30.110702609


Subproblem 2
x + -15 = -15.110702609

Simplifying
x + -15 = -15.110702609

Reorder the terms:
-15 + x = -15.110702609

Solving
-15 + x = -15.110702609

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -15.110702609 + 15

Combine like terms: -15 + 15 = 0
0 + x = -15.110702609 + 15
x = -15.110702609 + 15

Combine like terms: -15.110702609 + 15 = -0.110702609
x = -0.110702609

Simplifying
x = -0.110702609


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {30.110702609, -0.110702609}

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