3x^2+26x-50=0

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Solution for 3x^2+26x-50=0 equation: 


Simplifying
3x2 + 26x + -50 = 0

Reorder the terms:
-50 + 26x + 3x2 = 0

Solving
-50 + 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'.
-16.66666667 + 8.666666667x + x2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + 8.666666667x + 16.66666667 + x2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + 8.666666667x + x2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + 8.666666667x + x2 = 0 + 16.66666667
8.666666667x + x2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
8.666666667x + x2 = 16.66666667

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 = 16.66666667 + 18.77777778

Reorder the terms:
18.77777778 + 8.666666667x + x2 = 16.66666667 + 18.77777778

Combine like terms: 16.66666667 + 18.77777778 = 35.44444445
18.77777778 + 8.666666667x + x2 = 35.44444445

Factor a perfect square on the left side:
(x + 4.333333334)(x + 4.333333334) = 35.44444445

Calculate the square root of the right side: 5.9535237

Break this problem into two subproblems by setting 
(x + 4.333333334) equal to 5.9535237 and -5.9535237.


Subproblem 1
x + 4.333333334 = 5.9535237

Simplifying
x + 4.333333334 = 5.9535237

Reorder the terms:
4.333333334 + x = 5.9535237

Solving
4.333333334 + x = 5.9535237

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 = 5.9535237 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + x = 5.9535237 + -4.333333334
x = 5.9535237 + -4.333333334

Combine like terms: 5.9535237 + -4.333333334 = 1.620190366
x = 1.620190366

Simplifying
x = 1.620190366


Subproblem 2
x + 4.333333334 = -5.9535237

Simplifying
x + 4.333333334 = -5.9535237

Reorder the terms:
4.333333334 + x = -5.9535237

Solving
4.333333334 + x = -5.9535237

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 = -5.9535237 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + x = -5.9535237 + -4.333333334
x = -5.9535237 + -4.333333334

Combine like terms: -5.9535237 + -4.333333334 = -10.286857034
x = -10.286857034

Simplifying
x = -10.286857034


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.620190366, -10.286857034}

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