4x^2-22x-18=0

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Solution for 4x^2-22x-18=0 equation: 


Simplifying
4x2 + -22x + -18 = 0

Reorder the terms:
-18 + -22x + 4x2 = 0

Solving
-18 + -22x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -11x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + -11x + 2x2)' equal to zero and attempt to solve:

Simplifying
-9 + -11x + 2x2 = 0

Solving
-9 + -11x + 2x2 = 0

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

Divide each side by '2'.
-4.5 + -5.5x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -5.5x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -5.5x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -5.5x + x2 = 0 + 4.5
-5.5x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-5.5x + x2 = 4.5

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 4.5 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 4.5 + 7.5625

Combine like terms: 4.5 + 7.5625 = 12.0625
7.5625 + -5.5x + x2 = 12.0625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 12.0625

Calculate the square root of the right side: 3.473110997

Break this problem into two subproblems by setting 
(x + -2.75) equal to 3.473110997 and -3.473110997.


Subproblem 1
x + -2.75 = 3.473110997

Simplifying
x + -2.75 = 3.473110997

Reorder the terms:
-2.75 + x = 3.473110997

Solving
-2.75 + x = 3.473110997

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 3.473110997 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 3.473110997 + 2.75
x = 3.473110997 + 2.75

Combine like terms: 3.473110997 + 2.75 = 6.223110997
x = 6.223110997

Simplifying
x = 6.223110997


Subproblem 2
x + -2.75 = -3.473110997

Simplifying
x + -2.75 = -3.473110997

Reorder the terms:
-2.75 + x = -3.473110997

Solving
-2.75 + x = -3.473110997

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -3.473110997 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -3.473110997 + 2.75
x = -3.473110997 + 2.75

Combine like terms: -3.473110997 + 2.75 = -0.723110997
x = -0.723110997

Simplifying
x = -0.723110997


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.223110997, -0.723110997}
Solution
x = {6.223110997, -0.723110997}

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