3x^2-29x-26=0

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Solution for 3x^2-29x-26=0 equation: 


Simplifying
3x2 + -29x + -26 = 0

Reorder the terms:
-26 + -29x + 3x2 = 0

Solving
-26 + -29x + 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'.
-8.666666667 + -9.666666667x + x2 = 0

Move the constant term to the right:

Add '8.666666667' to each side of the equation.
-8.666666667 + -9.666666667x + 8.666666667 + x2 = 0 + 8.666666667

Reorder the terms:
-8.666666667 + 8.666666667 + -9.666666667x + x2 = 0 + 8.666666667

Combine like terms: -8.666666667 + 8.666666667 = 0.000000000
0.000000000 + -9.666666667x + x2 = 0 + 8.666666667
-9.666666667x + x2 = 0 + 8.666666667

Combine like terms: 0 + 8.666666667 = 8.666666667
-9.666666667x + x2 = 8.666666667

The x term is -9.666666667x.  Take half its coefficient (-4.833333334).
Square it (23.36111112) and add it to both sides.

Add '23.36111112' to each side of the equation.
-9.666666667x + 23.36111112 + x2 = 8.666666667 + 23.36111112

Reorder the terms:
23.36111112 + -9.666666667x + x2 = 8.666666667 + 23.36111112

Combine like terms: 8.666666667 + 23.36111112 = 32.027777787
23.36111112 + -9.666666667x + x2 = 32.027777787

Factor a perfect square on the left side:
(x + -4.833333334)(x + -4.833333334) = 32.027777787

Calculate the square root of the right side: 5.65930895

Break this problem into two subproblems by setting 
(x + -4.833333334) equal to 5.65930895 and -5.65930895.


Subproblem 1
x + -4.833333334 = 5.65930895

Simplifying
x + -4.833333334 = 5.65930895

Reorder the terms:
-4.833333334 + x = 5.65930895

Solving
-4.833333334 + x = 5.65930895

Solving for variable 'x'.

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

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + x = 5.65930895 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + x = 5.65930895 + 4.833333334
x = 5.65930895 + 4.833333334

Combine like terms: 5.65930895 + 4.833333334 = 10.492642284
x = 10.492642284

Simplifying
x = 10.492642284


Subproblem 2
x + -4.833333334 = -5.65930895

Simplifying
x + -4.833333334 = -5.65930895

Reorder the terms:
-4.833333334 + x = -5.65930895

Solving
-4.833333334 + x = -5.65930895

Solving for variable 'x'.

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

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + x = -5.65930895 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + x = -5.65930895 + 4.833333334
x = -5.65930895 + 4.833333334

Combine like terms: -5.65930895 + 4.833333334 = -0.825975616
x = -0.825975616

Simplifying
x = -0.825975616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.492642284, -0.825975616}

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