20=-85.6x^2+160x-9.35

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Solution for 20=-85.6x^2+160x-9.35 equation:


Simplifying
20 = -85.6x2 + 160x + -9.35

Reorder the terms:
20 = -9.35 + 160x + -85.6x2

Solving
20 = -9.35 + 160x + -85.6x2

Solving for variable 'x'.

Combine like terms: 20 + 9.35 = 29.35
29.35 + -160x + 85.6x2 = -9.35 + 160x + -85.6x2 + 9.35 + -160x + 85.6x2

Reorder the terms:
29.35 + -160x + 85.6x2 = -9.35 + 9.35 + 160x + -160x + -85.6x2 + 85.6x2

Combine like terms: -9.35 + 9.35 = 0.00
29.35 + -160x + 85.6x2 = 0.00 + 160x + -160x + -85.6x2 + 85.6x2
29.35 + -160x + 85.6x2 = 160x + -160x + -85.6x2 + 85.6x2

Combine like terms: 160x + -160x = 0
29.35 + -160x + 85.6x2 = 0 + -85.6x2 + 85.6x2
29.35 + -160x + 85.6x2 = -85.6x2 + 85.6x2

Combine like terms: -85.6x2 + 85.6x2 = 0.0
29.35 + -160x + 85.6x2 = 0.0

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

Divide each side by '85.6'.
0.3428738318 + -1.869158879x + x2 = 0

Move the constant term to the right:

Add '-0.3428738318' to each side of the equation.
0.3428738318 + -1.869158879x + -0.3428738318 + x2 = 0 + -0.3428738318

Reorder the terms:
0.3428738318 + -0.3428738318 + -1.869158879x + x2 = 0 + -0.3428738318

Combine like terms: 0.3428738318 + -0.3428738318 = 0.0000000000
0.0000000000 + -1.869158879x + x2 = 0 + -0.3428738318
-1.869158879x + x2 = 0 + -0.3428738318

Combine like terms: 0 + -0.3428738318 = -0.3428738318
-1.869158879x + x2 = -0.3428738318

The x term is -1.869158879x.  Take half its coefficient (-0.9345794395).
Square it (0.8734387287) and add it to both sides.

Add '0.8734387287' to each side of the equation.
-1.869158879x + 0.8734387287 + x2 = -0.3428738318 + 0.8734387287

Reorder the terms:
0.8734387287 + -1.869158879x + x2 = -0.3428738318 + 0.8734387287

Combine like terms: -0.3428738318 + 0.8734387287 = 0.5305648969
0.8734387287 + -1.869158879x + x2 = 0.5305648969

Factor a perfect square on the left side:
(x + -0.9345794395)(x + -0.9345794395) = 0.5305648969

Calculate the square root of the right side: 0.728398858

Break this problem into two subproblems by setting 
(x + -0.9345794395) equal to 0.728398858 and -0.728398858.

Subproblem 1

x + -0.9345794395 = 0.728398858 Simplifying x + -0.9345794395 = 0.728398858 Reorder the terms: -0.9345794395 + x = 0.728398858 Solving -0.9345794395 + x = 0.728398858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9345794395' to each side of the equation. -0.9345794395 + 0.9345794395 + x = 0.728398858 + 0.9345794395 Combine like terms: -0.9345794395 + 0.9345794395 = 0.0000000000 0.0000000000 + x = 0.728398858 + 0.9345794395 x = 0.728398858 + 0.9345794395 Combine like terms: 0.728398858 + 0.9345794395 = 1.6629782975 x = 1.6629782975 Simplifying x = 1.6629782975

Subproblem 2

x + -0.9345794395 = -0.728398858 Simplifying x + -0.9345794395 = -0.728398858 Reorder the terms: -0.9345794395 + x = -0.728398858 Solving -0.9345794395 + x = -0.728398858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9345794395' to each side of the equation. -0.9345794395 + 0.9345794395 + x = -0.728398858 + 0.9345794395 Combine like terms: -0.9345794395 + 0.9345794395 = 0.0000000000 0.0000000000 + x = -0.728398858 + 0.9345794395 x = -0.728398858 + 0.9345794395 Combine like terms: -0.728398858 + 0.9345794395 = 0.2061805815 x = 0.2061805815 Simplifying x = 0.2061805815

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.6629782975, 0.2061805815}

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