15x^2+70x-96=0

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Solution for 15x^2+70x-96=0 equation: 


Simplifying
15x2 + 70x + -96 = 0

Reorder the terms:
-96 + 70x + 15x2 = 0

Solving
-96 + 70x + 15x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
15 the coefficient of the squared term: 

Divide each side by '15'.
-6.4 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '6.4' to each side of the equation.
-6.4 + 4.666666667x + 6.4 + x2 = 0 + 6.4

Reorder the terms:
-6.4 + 6.4 + 4.666666667x + x2 = 0 + 6.4

Combine like terms: -6.4 + 6.4 = 0.0
0.0 + 4.666666667x + x2 = 0 + 6.4
4.666666667x + x2 = 0 + 6.4

Combine like terms: 0 + 6.4 = 6.4
4.666666667x + x2 = 6.4

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = 6.4 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 6.4 + 5.444444448

Combine like terms: 6.4 + 5.444444448 = 11.844444448
5.444444448 + 4.666666667x + x2 = 11.844444448

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 11.844444448

Calculate the square root of the right side: 3.441575867

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 3.441575867 and -3.441575867.


Subproblem 1
x + 2.333333334 = 3.441575867

Simplifying
x + 2.333333334 = 3.441575867

Reorder the terms:
2.333333334 + x = 3.441575867

Solving
2.333333334 + x = 3.441575867

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 3.441575867 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 3.441575867 + -2.333333334
x = 3.441575867 + -2.333333334

Combine like terms: 3.441575867 + -2.333333334 = 1.108242533
x = 1.108242533

Simplifying
x = 1.108242533


Subproblem 2
x + 2.333333334 = -3.441575867

Simplifying
x + 2.333333334 = -3.441575867

Reorder the terms:
2.333333334 + x = -3.441575867

Solving
2.333333334 + x = -3.441575867

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -3.441575867 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -3.441575867 + -2.333333334
x = -3.441575867 + -2.333333334

Combine like terms: -3.441575867 + -2.333333334 = -5.774909201
x = -5.774909201

Simplifying
x = -5.774909201


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.108242533, -5.774909201}

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