3x^2-26x-10=0

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Solution for 3x^2-26x-10=0 equation: 


Simplifying
3x2 + -26x + -10 = 0

Reorder the terms:
-10 + -26x + 3x2 = 0

Solving
-10 + -26x + 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 + -8.666666667x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -8.666666667x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -8.666666667x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -8.666666667x + x2 = 0 + 3.333333333
-8.666666667x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-8.666666667x + x2 = 3.333333333

The x term is -8.666666667x.  Take half its coefficient (-4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
-8.666666667x + 18.77777778 + x2 = 3.333333333 + 18.77777778

Reorder the terms:
18.77777778 + -8.666666667x + x2 = 3.333333333 + 18.77777778

Combine like terms: 3.333333333 + 18.77777778 = 22.111111113
18.77777778 + -8.666666667x + x2 = 22.111111113

Factor a perfect square on the left side:
(x + -4.333333334)(x + -4.333333334) = 22.111111113

Calculate the square root of the right side: 4.702245327

Break this problem into two subproblems by setting 
(x + -4.333333334) equal to 4.702245327 and -4.702245327.


Subproblem 1
x + -4.333333334 = 4.702245327

Simplifying
x + -4.333333334 = 4.702245327

Reorder the terms:
-4.333333334 + x = 4.702245327

Solving
-4.333333334 + x = 4.702245327

Solving for variable 'x'.

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

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + x = 4.702245327 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = 4.702245327 + 4.333333334
x = 4.702245327 + 4.333333334

Combine like terms: 4.702245327 + 4.333333334 = 9.035578661
x = 9.035578661

Simplifying
x = 9.035578661


Subproblem 2
x + -4.333333334 = -4.702245327

Simplifying
x + -4.333333334 = -4.702245327

Reorder the terms:
-4.333333334 + x = -4.702245327

Solving
-4.333333334 + x = -4.702245327

Solving for variable 'x'.

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

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + x = -4.702245327 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = -4.702245327 + 4.333333334
x = -4.702245327 + 4.333333334

Combine like terms: -4.702245327 + 4.333333334 = -0.368911993
x = -0.368911993

Simplifying
x = -0.368911993


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.035578661, -0.368911993}

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