15x^2+16x-1=0

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Solution for 15x^2+16x-1=0 equation: 


Simplifying
15x2 + 16x + -1 = 0

Reorder the terms:
-1 + 16x + 15x2 = 0

Solving
-1 + 16x + 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'.
-0.06666666667 + 1.066666667x + x2 = 0

Move the constant term to the right:

Add '0.06666666667' to each side of the equation.
-0.06666666667 + 1.066666667x + 0.06666666667 + x2 = 0 + 0.06666666667

Reorder the terms:
-0.06666666667 + 0.06666666667 + 1.066666667x + x2 = 0 + 0.06666666667

Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000
0.00000000000 + 1.066666667x + x2 = 0 + 0.06666666667
1.066666667x + x2 = 0 + 0.06666666667

Combine like terms: 0 + 0.06666666667 = 0.06666666667
1.066666667x + x2 = 0.06666666667

The x term is 1.066666667x.  Take half its coefficient (0.5333333335).
Square it (0.2844444446) and add it to both sides.

Add '0.2844444446' to each side of the equation.
1.066666667x + 0.2844444446 + x2 = 0.06666666667 + 0.2844444446

Reorder the terms:
0.2844444446 + 1.066666667x + x2 = 0.06666666667 + 0.2844444446

Combine like terms: 0.06666666667 + 0.2844444446 = 0.35111111127
0.2844444446 + 1.066666667x + x2 = 0.35111111127

Factor a perfect square on the left side:
(x + 0.5333333335)(x + 0.5333333335) = 0.35111111127

Calculate the square root of the right side: 0.592546295

Break this problem into two subproblems by setting 
(x + 0.5333333335) equal to 0.592546295 and -0.592546295.


Subproblem 1
x + 0.5333333335 = 0.592546295

Simplifying
x + 0.5333333335 = 0.592546295

Reorder the terms:
0.5333333335 + x = 0.592546295

Solving
0.5333333335 + x = 0.592546295

Solving for variable 'x'.

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

Add '-0.5333333335' to each side of the equation.
0.5333333335 + -0.5333333335 + x = 0.592546295 + -0.5333333335

Combine like terms: 0.5333333335 + -0.5333333335 = 0.0000000000
0.0000000000 + x = 0.592546295 + -0.5333333335
x = 0.592546295 + -0.5333333335

Combine like terms: 0.592546295 + -0.5333333335 = 0.0592129615
x = 0.0592129615

Simplifying
x = 0.0592129615


Subproblem 2
x + 0.5333333335 = -0.592546295

Simplifying
x + 0.5333333335 = -0.592546295

Reorder the terms:
0.5333333335 + x = -0.592546295

Solving
0.5333333335 + x = -0.592546295

Solving for variable 'x'.

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

Add '-0.5333333335' to each side of the equation.
0.5333333335 + -0.5333333335 + x = -0.592546295 + -0.5333333335

Combine like terms: 0.5333333335 + -0.5333333335 = 0.0000000000
0.0000000000 + x = -0.592546295 + -0.5333333335
x = -0.592546295 + -0.5333333335

Combine like terms: -0.592546295 + -0.5333333335 = -1.1258796285
x = -1.1258796285

Simplifying
x = -1.1258796285


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0592129615, -1.1258796285}

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