15x^2-7x-56=0

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Solution for 15x^2-7x-56=0 equation: 


Simplifying
15x2 + -7x + -56 = 0

Reorder the terms:
-56 + -7x + 15x2 = 0

Solving
-56 + -7x + 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'.
-3.733333333 + -0.4666666667x + x2 = 0

Move the constant term to the right:

Add '3.733333333' to each side of the equation.
-3.733333333 + -0.4666666667x + 3.733333333 + x2 = 0 + 3.733333333

Reorder the terms:
-3.733333333 + 3.733333333 + -0.4666666667x + x2 = 0 + 3.733333333

Combine like terms: -3.733333333 + 3.733333333 = 0.000000000
0.000000000 + -0.4666666667x + x2 = 0 + 3.733333333
-0.4666666667x + x2 = 0 + 3.733333333

Combine like terms: 0 + 3.733333333 = 3.733333333
-0.4666666667x + x2 = 3.733333333

The x term is -0.4666666667x.  Take half its coefficient (-0.2333333334).
Square it (0.05444444448) and add it to both sides.

Add '0.05444444448' to each side of the equation.
-0.4666666667x + 0.05444444448 + x2 = 3.733333333 + 0.05444444448

Reorder the terms:
0.05444444448 + -0.4666666667x + x2 = 3.733333333 + 0.05444444448

Combine like terms: 3.733333333 + 0.05444444448 = 3.78777777748
0.05444444448 + -0.4666666667x + x2 = 3.78777777748

Factor a perfect square on the left side:
(x + -0.2333333334)(x + -0.2333333334) = 3.78777777748

Calculate the square root of the right side: 1.94622141

Break this problem into two subproblems by setting 
(x + -0.2333333334) equal to 1.94622141 and -1.94622141.


Subproblem 1
x + -0.2333333334 = 1.94622141

Simplifying
x + -0.2333333334 = 1.94622141

Reorder the terms:
-0.2333333334 + x = 1.94622141

Solving
-0.2333333334 + x = 1.94622141

Solving for variable 'x'.

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

Add '0.2333333334' to each side of the equation.
-0.2333333334 + 0.2333333334 + x = 1.94622141 + 0.2333333334

Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000
0.0000000000 + x = 1.94622141 + 0.2333333334
x = 1.94622141 + 0.2333333334

Combine like terms: 1.94622141 + 0.2333333334 = 2.1795547434
x = 2.1795547434

Simplifying
x = 2.1795547434


Subproblem 2
x + -0.2333333334 = -1.94622141

Simplifying
x + -0.2333333334 = -1.94622141

Reorder the terms:
-0.2333333334 + x = -1.94622141

Solving
-0.2333333334 + x = -1.94622141

Solving for variable 'x'.

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

Add '0.2333333334' to each side of the equation.
-0.2333333334 + 0.2333333334 + x = -1.94622141 + 0.2333333334

Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000
0.0000000000 + x = -1.94622141 + 0.2333333334
x = -1.94622141 + 0.2333333334

Combine like terms: -1.94622141 + 0.2333333334 = -1.7128880766
x = -1.7128880766

Simplifying
x = -1.7128880766


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.1795547434, -1.7128880766}

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