3X^2+17X-8.7=0

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Solution for 3X^2+17X-8.7=0 equation: 


Simplifying
3X2 + 17X + -8.7 = 0

Reorder the terms:
-8.7 + 17X + 3X2 = 0

Solving
-8.7 + 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'.
-2.9 + 5.666666667X + X2 = 0

Move the constant term to the right:

Add '2.9' to each side of the equation.
-2.9 + 5.666666667X + 2.9 + X2 = 0 + 2.9

Reorder the terms:
-2.9 + 2.9 + 5.666666667X + X2 = 0 + 2.9

Combine like terms: -2.9 + 2.9 = 0.0
0.0 + 5.666666667X + X2 = 0 + 2.9
5.666666667X + X2 = 0 + 2.9

Combine like terms: 0 + 2.9 = 2.9
5.666666667X + X2 = 2.9

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 = 2.9 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667X + X2 = 2.9 + 8.027777782

Combine like terms: 2.9 + 8.027777782 = 10.927777782
8.027777782 + 5.666666667X + X2 = 10.927777782

Factor a perfect square on the left side:
(X + 2.833333334)(X + 2.833333334) = 10.927777782

Calculate the square root of the right side: 3.305718951

Break this problem into two subproblems by setting 
(X + 2.833333334) equal to 3.305718951 and -3.305718951.


Subproblem 1
X + 2.833333334 = 3.305718951

Simplifying
X + 2.833333334 = 3.305718951

Reorder the terms:
2.833333334 + X = 3.305718951

Solving
2.833333334 + X = 3.305718951

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 = 3.305718951 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + X = 3.305718951 + -2.833333334
X = 3.305718951 + -2.833333334

Combine like terms: 3.305718951 + -2.833333334 = 0.472385617
X = 0.472385617

Simplifying
X = 0.472385617


Subproblem 2
X + 2.833333334 = -3.305718951

Simplifying
X + 2.833333334 = -3.305718951

Reorder the terms:
2.833333334 + X = -3.305718951

Solving
2.833333334 + X = -3.305718951

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 = -3.305718951 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + X = -3.305718951 + -2.833333334
X = -3.305718951 + -2.833333334

Combine like terms: -3.305718951 + -2.833333334 = -6.139052285
X = -6.139052285

Simplifying
X = -6.139052285


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.472385617, -6.139052285}

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