4x^2+25x+15=0

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Solution for 4x^2+25x+15=0 equation: 


Simplifying
4x2 + 25x + 15 = 0

Reorder the terms:
15 + 25x + 4x2 = 0

Solving
15 + 25x + 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 + 6.25x + x2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + 6.25x + -3.75 + x2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + 6.25x + x2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + 6.25x + x2 = 0 + -3.75
6.25x + x2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
6.25x + x2 = -3.75

The x term is 6.25x.  Take half its coefficient (3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
6.25x + 9.765625 + x2 = -3.75 + 9.765625

Reorder the terms:
9.765625 + 6.25x + x2 = -3.75 + 9.765625

Combine like terms: -3.75 + 9.765625 = 6.015625
9.765625 + 6.25x + x2 = 6.015625

Factor a perfect square on the left side:
(x + 3.125)(x + 3.125) = 6.015625

Calculate the square root of the right side: 2.452677109

Break this problem into two subproblems by setting 
(x + 3.125) equal to 2.452677109 and -2.452677109.


Subproblem 1
x + 3.125 = 2.452677109

Simplifying
x + 3.125 = 2.452677109

Reorder the terms:
3.125 + x = 2.452677109

Solving
3.125 + x = 2.452677109

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = 2.452677109 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = 2.452677109 + -3.125
x = 2.452677109 + -3.125

Combine like terms: 2.452677109 + -3.125 = -0.672322891
x = -0.672322891

Simplifying
x = -0.672322891


Subproblem 2
x + 3.125 = -2.452677109

Simplifying
x + 3.125 = -2.452677109

Reorder the terms:
3.125 + x = -2.452677109

Solving
3.125 + x = -2.452677109

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = -2.452677109 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = -2.452677109 + -3.125
x = -2.452677109 + -3.125

Combine like terms: -2.452677109 + -3.125 = -5.577677109
x = -5.577677109

Simplifying
x = -5.577677109


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.672322891, -5.577677109}

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