20x+x^2=85.9375

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Solution for 20x+x^2=85.9375 equation: 


Simplifying
20x + x2 = 85.9375

Solving
20x + x2 = 85.9375

Solving for variable 'x'.

Reorder the terms:
-85.9375 + 20x + x2 = 85.9375 + -85.9375

Combine like terms: 85.9375 + -85.9375 = 0.0000
-85.9375 + 20x + x2 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '85.9375' to each side of the equation.
-85.9375 + 20x + 85.9375 + x2 = 0.0000 + 85.9375

Reorder the terms:
-85.9375 + 85.9375 + 20x + x2 = 0.0000 + 85.9375

Combine like terms: -85.9375 + 85.9375 = 0.0000
0.0000 + 20x + x2 = 0.0000 + 85.9375
20x + x2 = 0.0000 + 85.9375

Combine like terms: 0.0000 + 85.9375 = 85.9375
20x + x2 = 85.9375

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 85.9375 + 100

Reorder the terms:
100 + 20x + x2 = 85.9375 + 100

Combine like terms: 85.9375 + 100 = 185.9375
100 + 20x + x2 = 185.9375

Factor a perfect square on the left side:
(x + 10)(x + 10) = 185.9375

Calculate the square root of the right side: 13.635890143

Break this problem into two subproblems by setting 
(x + 10) equal to 13.635890143 and -13.635890143.


Subproblem 1
x + 10 = 13.635890143

Simplifying
x + 10 = 13.635890143

Reorder the terms:
10 + x = 13.635890143

Solving
10 + x = 13.635890143

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 13.635890143 + -10

Combine like terms: 10 + -10 = 0
0 + x = 13.635890143 + -10
x = 13.635890143 + -10

Combine like terms: 13.635890143 + -10 = 3.635890143
x = 3.635890143

Simplifying
x = 3.635890143


Subproblem 2
x + 10 = -13.635890143

Simplifying
x + 10 = -13.635890143

Reorder the terms:
10 + x = -13.635890143

Solving
10 + x = -13.635890143

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -13.635890143 + -10

Combine like terms: 10 + -10 = 0
0 + x = -13.635890143 + -10
x = -13.635890143 + -10

Combine like terms: -13.635890143 + -10 = -23.635890143
x = -23.635890143

Simplifying
x = -23.635890143


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.635890143, -23.635890143}

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