15x^2+14x-15=0

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


Simplifying
15x2 + 14x + -15 = 0

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

Solving
-15 + 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'.
-1 + 0.9333333333x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.9333333333x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.9333333333x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.9333333333x + x2 = 0 + 1
0.9333333333x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.9333333333x + x2 = 1

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 = 1 + 0.2177777778

Reorder the terms:
0.2177777778 + 0.9333333333x + x2 = 1 + 0.2177777778

Combine like terms: 1 + 0.2177777778 = 1.2177777778
0.2177777778 + 0.9333333333x + x2 = 1.2177777778

Factor a perfect square on the left side:
(x + 0.4666666667)(x + 0.4666666667) = 1.2177777778

Calculate the square root of the right side: 1.10352969

Break this problem into two subproblems by setting 
(x + 0.4666666667) equal to 1.10352969 and -1.10352969.


Subproblem 1
x + 0.4666666667 = 1.10352969

Simplifying
x + 0.4666666667 = 1.10352969

Reorder the terms:
0.4666666667 + x = 1.10352969

Solving
0.4666666667 + x = 1.10352969

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 = 1.10352969 + -0.4666666667

Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000
0.0000000000 + x = 1.10352969 + -0.4666666667
x = 1.10352969 + -0.4666666667

Combine like terms: 1.10352969 + -0.4666666667 = 0.6368630233
x = 0.6368630233

Simplifying
x = 0.6368630233


Subproblem 2
x + 0.4666666667 = -1.10352969

Simplifying
x + 0.4666666667 = -1.10352969

Reorder the terms:
0.4666666667 + x = -1.10352969

Solving
0.4666666667 + x = -1.10352969

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 = -1.10352969 + -0.4666666667

Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000
0.0000000000 + x = -1.10352969 + -0.4666666667
x = -1.10352969 + -0.4666666667

Combine like terms: -1.10352969 + -0.4666666667 = -1.5701963567
x = -1.5701963567

Simplifying
x = -1.5701963567


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6368630233, -1.5701963567}

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