-16x^2+175x-85=0

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Solution for -16x^2+175x-85=0 equation:


Simplifying
-16x2 + 175x + -85 = 0

Reorder the terms:
-85 + 175x + -16x2 = 0

Solving
-85 + 175x + -16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
5.3125 + -10.9375x + x2 = 0

Move the constant term to the right:

Add '-5.3125' to each side of the equation.
5.3125 + -10.9375x + -5.3125 + x2 = 0 + -5.3125

Reorder the terms:
5.3125 + -5.3125 + -10.9375x + x2 = 0 + -5.3125

Combine like terms: 5.3125 + -5.3125 = 0.0000
0.0000 + -10.9375x + x2 = 0 + -5.3125
-10.9375x + x2 = 0 + -5.3125

Combine like terms: 0 + -5.3125 = -5.3125
-10.9375x + x2 = -5.3125

The x term is -10.9375x.  Take half its coefficient (-5.46875).
Square it (29.90722656) and add it to both sides.

Add '29.90722656' to each side of the equation.
-10.9375x + 29.90722656 + x2 = -5.3125 + 29.90722656

Reorder the terms:
29.90722656 + -10.9375x + x2 = -5.3125 + 29.90722656

Combine like terms: -5.3125 + 29.90722656 = 24.59472656
29.90722656 + -10.9375x + x2 = 24.59472656

Factor a perfect square on the left side:
(x + -5.46875)(x + -5.46875) = 24.59472656

Calculate the square root of the right side: 4.959307065

Break this problem into two subproblems by setting 
(x + -5.46875) equal to 4.959307065 and -4.959307065.


Subproblem 1
x + -5.46875 = 4.959307065

Simplifying
x + -5.46875 = 4.959307065

Reorder the terms:
-5.46875 + x = 4.959307065

Solving
-5.46875 + x = 4.959307065

Solving for variable 'x'.

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

Add '5.46875' to each side of the equation.
-5.46875 + 5.46875 + x = 4.959307065 + 5.46875

Combine like terms: -5.46875 + 5.46875 = 0.00000
0.00000 + x = 4.959307065 + 5.46875
x = 4.959307065 + 5.46875

Combine like terms: 4.959307065 + 5.46875 = 10.428057065
x = 10.428057065

Simplifying
x = 10.428057065


Subproblem 2
x + -5.46875 = -4.959307065

Simplifying
x + -5.46875 = -4.959307065

Reorder the terms:
-5.46875 + x = -4.959307065

Solving
-5.46875 + x = -4.959307065

Solving for variable 'x'.

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

Add '5.46875' to each side of the equation.
-5.46875 + 5.46875 + x = -4.959307065 + 5.46875

Combine like terms: -5.46875 + 5.46875 = 0.00000
0.00000 + x = -4.959307065 + 5.46875
x = -4.959307065 + 5.46875

Combine like terms: -4.959307065 + 5.46875 = 0.509442935
x = 0.509442935

Simplifying
x = 0.509442935


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.428057065, 0.509442935}

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