3x^2-26x-75=0

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Solution for 3x^2-26x-75=0 equation: 


Simplifying
3x2 + -26x + -75 = 0

Reorder the terms:
-75 + -26x + 3x2 = 0

Solving
-75 + -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'.
-25 + -8.666666667x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -8.666666667x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -8.666666667x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -8.666666667x + x2 = 0 + 25
-8.666666667x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-8.666666667x + x2 = 25

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 = 25 + 18.77777778

Reorder the terms:
18.77777778 + -8.666666667x + x2 = 25 + 18.77777778

Combine like terms: 25 + 18.77777778 = 43.77777778
18.77777778 + -8.666666667x + x2 = 43.77777778

Factor a perfect square on the left side:
(x + -4.333333334)(x + -4.333333334) = 43.77777778

Calculate the square root of the right side: 6.616477747

Break this problem into two subproblems by setting 
(x + -4.333333334) equal to 6.616477747 and -6.616477747.


Subproblem 1
x + -4.333333334 = 6.616477747

Simplifying
x + -4.333333334 = 6.616477747

Reorder the terms:
-4.333333334 + x = 6.616477747

Solving
-4.333333334 + x = 6.616477747

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 = 6.616477747 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = 6.616477747 + 4.333333334
x = 6.616477747 + 4.333333334

Combine like terms: 6.616477747 + 4.333333334 = 10.949811081
x = 10.949811081

Simplifying
x = 10.949811081


Subproblem 2
x + -4.333333334 = -6.616477747

Simplifying
x + -4.333333334 = -6.616477747

Reorder the terms:
-4.333333334 + x = -6.616477747

Solving
-4.333333334 + x = -6.616477747

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 = -6.616477747 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = -6.616477747 + 4.333333334
x = -6.616477747 + 4.333333334

Combine like terms: -6.616477747 + 4.333333334 = -2.283144413
x = -2.283144413

Simplifying
x = -2.283144413


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.949811081, -2.283144413}

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