15.6765+14.93x-165x^2=0

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Solution for 15.6765+14.93x-165x^2=0 equation: 


Simplifying
15.6765 + 14.93x + -165x2 = 0

Solving
15.6765 + 14.93x + -165x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-165 the coefficient of the squared term: 

Divide each side by '-165'.
-0.09500909091 + -0.09048484848x + x2 = 0

Move the constant term to the right:

Add '0.09500909091' to each side of the equation.
-0.09500909091 + -0.09048484848x + 0.09500909091 + x2 = 0 + 0.09500909091

Reorder the terms:
-0.09500909091 + 0.09500909091 + -0.09048484848x + x2 = 0 + 0.09500909091

Combine like terms: -0.09500909091 + 0.09500909091 = 0.00000000000
0.00000000000 + -0.09048484848x + x2 = 0 + 0.09500909091
-0.09048484848x + x2 = 0 + 0.09500909091

Combine like terms: 0 + 0.09500909091 = 0.09500909091
-0.09048484848x + x2 = 0.09500909091

The x term is -0.09048484848x.  Take half its coefficient (-0.04524242424).
Square it (0.002046876951) and add it to both sides.

Add '0.002046876951' to each side of the equation.
-0.09048484848x + 0.002046876951 + x2 = 0.09500909091 + 0.002046876951

Reorder the terms:
0.002046876951 + -0.09048484848x + x2 = 0.09500909091 + 0.002046876951

Combine like terms: 0.09500909091 + 0.002046876951 = 0.097055967861
0.002046876951 + -0.09048484848x + x2 = 0.097055967861

Factor a perfect square on the left side:
(x + -0.04524242424)(x + -0.04524242424) = 0.097055967861

Calculate the square root of the right side: 0.311538068

Break this problem into two subproblems by setting 
(x + -0.04524242424) equal to 0.311538068 and -0.311538068.


Subproblem 1
x + -0.04524242424 = 0.311538068

Simplifying
x + -0.04524242424 = 0.311538068

Reorder the terms:
-0.04524242424 + x = 0.311538068

Solving
-0.04524242424 + x = 0.311538068

Solving for variable 'x'.

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

Add '0.04524242424' to each side of the equation.
-0.04524242424 + 0.04524242424 + x = 0.311538068 + 0.04524242424

Combine like terms: -0.04524242424 + 0.04524242424 = 0.00000000000
0.00000000000 + x = 0.311538068 + 0.04524242424
x = 0.311538068 + 0.04524242424

Combine like terms: 0.311538068 + 0.04524242424 = 0.35678049224
x = 0.35678049224

Simplifying
x = 0.35678049224


Subproblem 2
x + -0.04524242424 = -0.311538068

Simplifying
x + -0.04524242424 = -0.311538068

Reorder the terms:
-0.04524242424 + x = -0.311538068

Solving
-0.04524242424 + x = -0.311538068

Solving for variable 'x'.

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

Add '0.04524242424' to each side of the equation.
-0.04524242424 + 0.04524242424 + x = -0.311538068 + 0.04524242424

Combine like terms: -0.04524242424 + 0.04524242424 = 0.00000000000
0.00000000000 + x = -0.311538068 + 0.04524242424
x = -0.311538068 + 0.04524242424

Combine like terms: -0.311538068 + 0.04524242424 = -0.26629564376
x = -0.26629564376

Simplifying
x = -0.26629564376


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.35678049224, -0.26629564376}

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