3x^2-80x-40=

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Solution for 3x^2-80x-40= equation: 


Simplifying
3x2 + -80x + -40 = 0

Reorder the terms:
-40 + -80x + 3x2 = 0

Solving
-40 + -80x + 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'.
-13.33333333 + -26.66666667x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -26.66666667x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -26.66666667x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -26.66666667x + x2 = 0 + 13.33333333
-26.66666667x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-26.66666667x + x2 = 13.33333333

The x term is -26.66666667x.  Take half its coefficient (-13.33333334).
Square it (177.7777780) and add it to both sides.

Add '177.7777780' to each side of the equation.
-26.66666667x + 177.7777780 + x2 = 13.33333333 + 177.7777780

Reorder the terms:
177.7777780 + -26.66666667x + x2 = 13.33333333 + 177.7777780

Combine like terms: 13.33333333 + 177.7777780 = 191.11111133
177.7777780 + -26.66666667x + x2 = 191.11111133

Factor a perfect square on the left side:
(x + -13.33333334)(x + -13.33333334) = 191.11111133

Calculate the square root of the right side: 13.824294243

Break this problem into two subproblems by setting 
(x + -13.33333334) equal to 13.824294243 and -13.824294243.


Subproblem 1
x + -13.33333334 = 13.824294243

Simplifying
x + -13.33333334 = 13.824294243

Reorder the terms:
-13.33333334 + x = 13.824294243

Solving
-13.33333334 + x = 13.824294243

Solving for variable 'x'.

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

Add '13.33333334' to each side of the equation.
-13.33333334 + 13.33333334 + x = 13.824294243 + 13.33333334

Combine like terms: -13.33333334 + 13.33333334 = 0.00000000
0.00000000 + x = 13.824294243 + 13.33333334
x = 13.824294243 + 13.33333334

Combine like terms: 13.824294243 + 13.33333334 = 27.157627583
x = 27.157627583

Simplifying
x = 27.157627583


Subproblem 2
x + -13.33333334 = -13.824294243

Simplifying
x + -13.33333334 = -13.824294243

Reorder the terms:
-13.33333334 + x = -13.824294243

Solving
-13.33333334 + x = -13.824294243

Solving for variable 'x'.

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

Add '13.33333334' to each side of the equation.
-13.33333334 + 13.33333334 + x = -13.824294243 + 13.33333334

Combine like terms: -13.33333334 + 13.33333334 = 0.00000000
0.00000000 + x = -13.824294243 + 13.33333334
x = -13.824294243 + 13.33333334

Combine like terms: -13.824294243 + 13.33333334 = -0.490960903
x = -0.490960903

Simplifying
x = -0.490960903


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.157627583, -0.490960903}

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