5x^2-90x-100=0

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Solution for 5x^2-90x-100=0 equation: 


Simplifying
5x2 + -90x + -100 = 0

Reorder the terms:
-100 + -90x + 5x2 = 0

Solving
-100 + -90x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-20 + -18x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-20 + -18x + x2)' equal to zero and attempt to solve:

Simplifying
-20 + -18x + x2 = 0

Solving
-20 + -18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -18x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -18x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -18x + x2 = 0 + 20
-18x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-18x + x2 = 20

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = 20 + 81

Reorder the terms:
81 + -18x + x2 = 20 + 81

Combine like terms: 20 + 81 = 101
81 + -18x + x2 = 101

Factor a perfect square on the left side:
(x + -9)(x + -9) = 101

Calculate the square root of the right side: 10.049875621

Break this problem into two subproblems by setting 
(x + -9) equal to 10.049875621 and -10.049875621.


Subproblem 1
x + -9 = 10.049875621

Simplifying
x + -9 = 10.049875621

Reorder the terms:
-9 + x = 10.049875621

Solving
-9 + x = 10.049875621

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = 10.049875621 + 9

Combine like terms: -9 + 9 = 0
0 + x = 10.049875621 + 9
x = 10.049875621 + 9

Combine like terms: 10.049875621 + 9 = 19.049875621
x = 19.049875621

Simplifying
x = 19.049875621


Subproblem 2
x + -9 = -10.049875621

Simplifying
x + -9 = -10.049875621

Reorder the terms:
-9 + x = -10.049875621

Solving
-9 + x = -10.049875621

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = -10.049875621 + 9

Combine like terms: -9 + 9 = 0
0 + x = -10.049875621 + 9
x = -10.049875621 + 9

Combine like terms: -10.049875621 + 9 = -1.049875621
x = -1.049875621

Simplifying
x = -1.049875621


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.049875621, -1.049875621}
Solution
x = {19.049875621, -1.049875621}

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