4x^2-30x-22=0

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Solution for 4x^2-30x-22=0 equation: 


Simplifying
4x2 + -30x + -22 = 0

Reorder the terms:
-22 + -30x + 4x2 = 0

Solving
-22 + -30x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + -15x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11 + -15x + 2x2)' equal to zero and attempt to solve:

Simplifying
-11 + -15x + 2x2 = 0

Solving
-11 + -15x + 2x2 = 0

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

Divide each side by '2'.
-5.5 + -7.5x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -7.5x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -7.5x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -7.5x + x2 = 0 + 5.5
-7.5x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-7.5x + x2 = 5.5

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = 5.5 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = 5.5 + 14.0625

Combine like terms: 5.5 + 14.0625 = 19.5625
14.0625 + -7.5x + x2 = 19.5625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 19.5625

Calculate the square root of the right side: 4.422951503

Break this problem into two subproblems by setting 
(x + -3.75) equal to 4.422951503 and -4.422951503.


Subproblem 1
x + -3.75 = 4.422951503

Simplifying
x + -3.75 = 4.422951503

Reorder the terms:
-3.75 + x = 4.422951503

Solving
-3.75 + x = 4.422951503

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 4.422951503 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 4.422951503 + 3.75
x = 4.422951503 + 3.75

Combine like terms: 4.422951503 + 3.75 = 8.172951503
x = 8.172951503

Simplifying
x = 8.172951503


Subproblem 2
x + -3.75 = -4.422951503

Simplifying
x + -3.75 = -4.422951503

Reorder the terms:
-3.75 + x = -4.422951503

Solving
-3.75 + x = -4.422951503

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -4.422951503 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -4.422951503 + 3.75
x = -4.422951503 + 3.75

Combine like terms: -4.422951503 + 3.75 = -0.672951503
x = -0.672951503

Simplifying
x = -0.672951503


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.172951503, -0.672951503}
Solution
x = {8.172951503, -0.672951503}

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