4x^2-30x-110=0

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Solution for 4x^2-30x-110=0 equation: 


Simplifying
4x2 + -30x + -110 = 0

Reorder the terms:
-110 + -30x + 4x2 = 0

Solving
-110 + -30x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-55 + -15x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-55 + -15x + 2x2)' equal to zero and attempt to solve:

Simplifying
-55 + -15x + 2x2 = 0

Solving
-55 + -15x + 2x2 = 0

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

Divide each side by '2'.
-27.5 + -7.5x + x2 = 0

Move the constant term to the right:

Add '27.5' to each side of the equation.
-27.5 + -7.5x + 27.5 + x2 = 0 + 27.5

Reorder the terms:
-27.5 + 27.5 + -7.5x + x2 = 0 + 27.5

Combine like terms: -27.5 + 27.5 = 0.0
0.0 + -7.5x + x2 = 0 + 27.5
-7.5x + x2 = 0 + 27.5

Combine like terms: 0 + 27.5 = 27.5
-7.5x + x2 = 27.5

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 = 27.5 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = 27.5 + 14.0625

Combine like terms: 27.5 + 14.0625 = 41.5625
14.0625 + -7.5x + x2 = 41.5625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 41.5625

Calculate the square root of the right side: 6.446898479

Break this problem into two subproblems by setting 
(x + -3.75) equal to 6.446898479 and -6.446898479.


Subproblem 1
x + -3.75 = 6.446898479

Simplifying
x + -3.75 = 6.446898479

Reorder the terms:
-3.75 + x = 6.446898479

Solving
-3.75 + x = 6.446898479

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 = 6.446898479 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 6.446898479 + 3.75
x = 6.446898479 + 3.75

Combine like terms: 6.446898479 + 3.75 = 10.196898479
x = 10.196898479

Simplifying
x = 10.196898479


Subproblem 2
x + -3.75 = -6.446898479

Simplifying
x + -3.75 = -6.446898479

Reorder the terms:
-3.75 + x = -6.446898479

Solving
-3.75 + x = -6.446898479

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 = -6.446898479 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -6.446898479 + 3.75
x = -6.446898479 + 3.75

Combine like terms: -6.446898479 + 3.75 = -2.696898479
x = -2.696898479

Simplifying
x = -2.696898479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.196898479, -2.696898479}
Solution
x = {10.196898479, -2.696898479}

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