4x^2+30x-1188=0

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Solution for 4x^2+30x-1188=0 equation: 


Simplifying
4x2 + 30x + -1188 = 0

Reorder the terms:
-1188 + 30x + 4x2 = 0

Solving
-1188 + 30x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-594 + 15x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-594 + 15x + 2x2)' equal to zero and attempt to solve:

Simplifying
-594 + 15x + 2x2 = 0

Solving
-594 + 15x + 2x2 = 0

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

Divide each side by '2'.
-297 + 7.5x + x2 = 0

Move the constant term to the right:

Add '297' to each side of the equation.
-297 + 7.5x + 297 + x2 = 0 + 297

Reorder the terms:
-297 + 297 + 7.5x + x2 = 0 + 297

Combine like terms: -297 + 297 = 0
0 + 7.5x + x2 = 0 + 297
7.5x + x2 = 0 + 297

Combine like terms: 0 + 297 = 297
7.5x + x2 = 297

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 = 297 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 297 + 14.0625

Combine like terms: 297 + 14.0625 = 311.0625
14.0625 + 7.5x + x2 = 311.0625

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 311.0625

Calculate the square root of the right side: 17.636964024

Break this problem into two subproblems by setting 
(x + 3.75) equal to 17.636964024 and -17.636964024.


Subproblem 1
x + 3.75 = 17.636964024

Simplifying
x + 3.75 = 17.636964024

Reorder the terms:
3.75 + x = 17.636964024

Solving
3.75 + x = 17.636964024

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 = 17.636964024 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 17.636964024 + -3.75
x = 17.636964024 + -3.75

Combine like terms: 17.636964024 + -3.75 = 13.886964024
x = 13.886964024

Simplifying
x = 13.886964024


Subproblem 2
x + 3.75 = -17.636964024

Simplifying
x + 3.75 = -17.636964024

Reorder the terms:
3.75 + x = -17.636964024

Solving
3.75 + x = -17.636964024

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 = -17.636964024 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -17.636964024 + -3.75
x = -17.636964024 + -3.75

Combine like terms: -17.636964024 + -3.75 = -21.386964024
x = -21.386964024

Simplifying
x = -21.386964024


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.886964024, -21.386964024}
Solution
x = {13.886964024, -21.386964024}

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