-4x^2+20x-18=0

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Solution for -4x^2+20x-18=0 equation: 


Simplifying
-4x2 + 20x + -18 = 0

Reorder the terms:
-18 + 20x + -4x2 = 0

Solving
-18 + 20x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 10x + -2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + 10x + -2x2)' equal to zero and attempt to solve:

Simplifying
-9 + 10x + -2x2 = 0

Solving
-9 + 10x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
4.5 + -5x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -5x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -5x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -5x + x2 = 0 + -4.5
-5x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-5x + x2 = -4.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -4.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -4.5 + 6.25

Combine like terms: -4.5 + 6.25 = 1.75
6.25 + -5x + x2 = 1.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.322875656 and -1.322875656.


Subproblem 1
x + -2.5 = 1.322875656

Simplifying
x + -2.5 = 1.322875656

Reorder the terms:
-2.5 + x = 1.322875656

Solving
-2.5 + x = 1.322875656

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 1.322875656 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.322875656 + 2.5
x = 1.322875656 + 2.5

Combine like terms: 1.322875656 + 2.5 = 3.822875656
x = 3.822875656

Simplifying
x = 3.822875656


Subproblem 2
x + -2.5 = -1.322875656

Simplifying
x + -2.5 = -1.322875656

Reorder the terms:
-2.5 + x = -1.322875656

Solving
-2.5 + x = -1.322875656

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -1.322875656 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.322875656 + 2.5
x = -1.322875656 + 2.5

Combine like terms: -1.322875656 + 2.5 = 1.177124344
x = 1.177124344

Simplifying
x = 1.177124344


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.822875656, 1.177124344}
Solution
x = {3.822875656, 1.177124344}

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