15x^2-14x-57=0

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Solution for 15x^2-14x-57=0 equation: 


Simplifying
15x2 + -14x + -57 = 0

Reorder the terms:
-57 + -14x + 15x2 = 0

Solving
-57 + -14x + 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'.
-3.8 + -0.9333333333x + x2 = 0

Move the constant term to the right:

Add '3.8' to each side of the equation.
-3.8 + -0.9333333333x + 3.8 + x2 = 0 + 3.8

Reorder the terms:
-3.8 + 3.8 + -0.9333333333x + x2 = 0 + 3.8

Combine like terms: -3.8 + 3.8 = 0.0
0.0 + -0.9333333333x + x2 = 0 + 3.8
-0.9333333333x + x2 = 0 + 3.8

Combine like terms: 0 + 3.8 = 3.8
-0.9333333333x + x2 = 3.8

The x term is -0.9333333333x.  Take half its coefficient (-0.4666666667).
Square it (0.2177777778) and add it to both sides.

Add '0.2177777778' to each side of the equation.
-0.9333333333x + 0.2177777778 + x2 = 3.8 + 0.2177777778

Reorder the terms:
0.2177777778 + -0.9333333333x + x2 = 3.8 + 0.2177777778

Combine like terms: 3.8 + 0.2177777778 = 4.0177777778
0.2177777778 + -0.9333333333x + x2 = 4.0177777778

Factor a perfect square on the left side:
(x + -0.4666666667)(x + -0.4666666667) = 4.0177777778

Calculate the square root of the right side: 2.004439517

Break this problem into two subproblems by setting 
(x + -0.4666666667) equal to 2.004439517 and -2.004439517.


Subproblem 1
x + -0.4666666667 = 2.004439517

Simplifying
x + -0.4666666667 = 2.004439517

Reorder the terms:
-0.4666666667 + x = 2.004439517

Solving
-0.4666666667 + x = 2.004439517

Solving for variable 'x'.

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

Add '0.4666666667' to each side of the equation.
-0.4666666667 + 0.4666666667 + x = 2.004439517 + 0.4666666667

Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000
0.0000000000 + x = 2.004439517 + 0.4666666667
x = 2.004439517 + 0.4666666667

Combine like terms: 2.004439517 + 0.4666666667 = 2.4711061837
x = 2.4711061837

Simplifying
x = 2.4711061837


Subproblem 2
x + -0.4666666667 = -2.004439517

Simplifying
x + -0.4666666667 = -2.004439517

Reorder the terms:
-0.4666666667 + x = -2.004439517

Solving
-0.4666666667 + x = -2.004439517

Solving for variable 'x'.

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

Add '0.4666666667' to each side of the equation.
-0.4666666667 + 0.4666666667 + x = -2.004439517 + 0.4666666667

Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000
0.0000000000 + x = -2.004439517 + 0.4666666667
x = -2.004439517 + 0.4666666667

Combine like terms: -2.004439517 + 0.4666666667 = -1.5377728503
x = -1.5377728503

Simplifying
x = -1.5377728503


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.4711061837, -1.5377728503}

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