3x^2+17x-7.5=0

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Solution for 3x^2+17x-7.5=0 equation: 


Simplifying
3x2 + 17x + -7.5 = 0

Reorder the terms:
-7.5 + 17x + 3x2 = 0

Solving
-7.5 + 17x + 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'.
-2.5 + 5.666666667x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 5.666666667x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 5.666666667x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 5.666666667x + x2 = 0 + 2.5
5.666666667x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
5.666666667x + x2 = 2.5

The x term is 5.666666667x.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667x + 8.027777782 + x2 = 2.5 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667x + x2 = 2.5 + 8.027777782

Combine like terms: 2.5 + 8.027777782 = 10.527777782
8.027777782 + 5.666666667x + x2 = 10.527777782

Factor a perfect square on the left side:
(x + 2.833333334)(x + 2.833333334) = 10.527777782

Calculate the square root of the right side: 3.244653723

Break this problem into two subproblems by setting 
(x + 2.833333334) equal to 3.244653723 and -3.244653723.


Subproblem 1
x + 2.833333334 = 3.244653723

Simplifying
x + 2.833333334 = 3.244653723

Reorder the terms:
2.833333334 + x = 3.244653723

Solving
2.833333334 + x = 3.244653723

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = 3.244653723 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = 3.244653723 + -2.833333334
x = 3.244653723 + -2.833333334

Combine like terms: 3.244653723 + -2.833333334 = 0.411320389
x = 0.411320389

Simplifying
x = 0.411320389


Subproblem 2
x + 2.833333334 = -3.244653723

Simplifying
x + 2.833333334 = -3.244653723

Reorder the terms:
2.833333334 + x = -3.244653723

Solving
2.833333334 + x = -3.244653723

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = -3.244653723 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = -3.244653723 + -2.833333334
x = -3.244653723 + -2.833333334

Combine like terms: -3.244653723 + -2.833333334 = -6.077987057
x = -6.077987057

Simplifying
x = -6.077987057


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.411320389, -6.077987057}

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