4x^2+27x+15=0

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Solution for 4x^2+27x+15=0 equation: 


Simplifying
4x2 + 27x + 15 = 0

Reorder the terms:
15 + 27x + 4x2 = 0

Solving
15 + 27x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
3.75 + 6.75x + x2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + 6.75x + -3.75 + x2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + 6.75x + x2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + 6.75x + x2 = 0 + -3.75
6.75x + x2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
6.75x + x2 = -3.75

The x term is 6.75x.  Take half its coefficient (3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
6.75x + 11.390625 + x2 = -3.75 + 11.390625

Reorder the terms:
11.390625 + 6.75x + x2 = -3.75 + 11.390625

Combine like terms: -3.75 + 11.390625 = 7.640625
11.390625 + 6.75x + x2 = 7.640625

Factor a perfect square on the left side:
(x + 3.375)(x + 3.375) = 7.640625

Calculate the square root of the right side: 2.764168048

Break this problem into two subproblems by setting 
(x + 3.375) equal to 2.764168048 and -2.764168048.


Subproblem 1
x + 3.375 = 2.764168048

Simplifying
x + 3.375 = 2.764168048

Reorder the terms:
3.375 + x = 2.764168048

Solving
3.375 + x = 2.764168048

Solving for variable 'x'.

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

Add '-3.375' to each side of the equation.
3.375 + -3.375 + x = 2.764168048 + -3.375

Combine like terms: 3.375 + -3.375 = 0.000
0.000 + x = 2.764168048 + -3.375
x = 2.764168048 + -3.375

Combine like terms: 2.764168048 + -3.375 = -0.610831952
x = -0.610831952

Simplifying
x = -0.610831952


Subproblem 2
x + 3.375 = -2.764168048

Simplifying
x + 3.375 = -2.764168048

Reorder the terms:
3.375 + x = -2.764168048

Solving
3.375 + x = -2.764168048

Solving for variable 'x'.

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

Add '-3.375' to each side of the equation.
3.375 + -3.375 + x = -2.764168048 + -3.375

Combine like terms: 3.375 + -3.375 = 0.000
0.000 + x = -2.764168048 + -3.375
x = -2.764168048 + -3.375

Combine like terms: -2.764168048 + -3.375 = -6.139168048
x = -6.139168048

Simplifying
x = -6.139168048


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.610831952, -6.139168048}

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