4x^2+30x+8=0

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Solution for 4x^2+30x+8=0 equation: 


Simplifying
4x2 + 30x + 8 = 0

Reorder the terms:
8 + 30x + 4x2 = 0

Solving
8 + 30x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 15x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + 15x + 2x2)' equal to zero and attempt to solve:

Simplifying
4 + 15x + 2x2 = 0

Solving
4 + 15x + 2x2 = 0

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

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

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 7.5x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 7.5x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7.5x + x2 = 0 + -2
7.5x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
7.5x + x2 = -2

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 = -2 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = -2 + 14.0625

Combine like terms: -2 + 14.0625 = 12.0625
14.0625 + 7.5x + x2 = 12.0625

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 12.0625

Calculate the square root of the right side: 3.473110997

Break this problem into two subproblems by setting 
(x + 3.75) equal to 3.473110997 and -3.473110997.


Subproblem 1
x + 3.75 = 3.473110997

Simplifying
x + 3.75 = 3.473110997

Reorder the terms:
3.75 + x = 3.473110997

Solving
3.75 + x = 3.473110997

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 = 3.473110997 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 3.473110997 + -3.75
x = 3.473110997 + -3.75

Combine like terms: 3.473110997 + -3.75 = -0.276889003
x = -0.276889003

Simplifying
x = -0.276889003


Subproblem 2
x + 3.75 = -3.473110997

Simplifying
x + 3.75 = -3.473110997

Reorder the terms:
3.75 + x = -3.473110997

Solving
3.75 + x = -3.473110997

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 = -3.473110997 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -3.473110997 + -3.75
x = -3.473110997 + -3.75

Combine like terms: -3.473110997 + -3.75 = -7.223110997
x = -7.223110997

Simplifying
x = -7.223110997


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.276889003, -7.223110997}
Solution
x = {-0.276889003, -7.223110997}

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