4x^2-30x-4=0

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


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

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

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

Solving for variable 'x'.

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

Ignore the factor 2.

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

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

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

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

Divide each side by '2'.
-1 + -7.5x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -7.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -7.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7.5x + x2 = 0 + 1
-7.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-7.5x + x2 = 1

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 = 1 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = 1 + 14.0625

Combine like terms: 1 + 14.0625 = 15.0625
14.0625 + -7.5x + x2 = 15.0625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 15.0625

Calculate the square root of the right side: 3.881043674

Break this problem into two subproblems by setting 
(x + -3.75) equal to 3.881043674 and -3.881043674.


Subproblem 1
x + -3.75 = 3.881043674

Simplifying
x + -3.75 = 3.881043674

Reorder the terms:
-3.75 + x = 3.881043674

Solving
-3.75 + x = 3.881043674

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 = 3.881043674 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 3.881043674 + 3.75
x = 3.881043674 + 3.75

Combine like terms: 3.881043674 + 3.75 = 7.631043674
x = 7.631043674

Simplifying
x = 7.631043674


Subproblem 2
x + -3.75 = -3.881043674

Simplifying
x + -3.75 = -3.881043674

Reorder the terms:
-3.75 + x = -3.881043674

Solving
-3.75 + x = -3.881043674

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 = -3.881043674 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -3.881043674 + 3.75
x = -3.881043674 + 3.75

Combine like terms: -3.881043674 + 3.75 = -0.131043674
x = -0.131043674

Simplifying
x = -0.131043674


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.631043674, -0.131043674}
Solution
x = {7.631043674, -0.131043674}

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