4x^2+21x+15=0

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Solution for 4x^2+21x+15=0 equation: 


Simplifying
4x2 + 21x + 15 = 0

Reorder the terms:
15 + 21x + 4x2 = 0

Solving
15 + 21x + 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 + 5.25x + x2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + 5.25x + -3.75 + x2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + 5.25x + x2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + 5.25x + x2 = 0 + -3.75
5.25x + x2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
5.25x + x2 = -3.75

The x term is 5.25x.  Take half its coefficient (2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
5.25x + 6.890625 + x2 = -3.75 + 6.890625

Reorder the terms:
6.890625 + 5.25x + x2 = -3.75 + 6.890625

Combine like terms: -3.75 + 6.890625 = 3.140625
6.890625 + 5.25x + x2 = 3.140625

Factor a perfect square on the left side:
(x + 2.625)(x + 2.625) = 3.140625

Calculate the square root of the right side: 1.77218086

Break this problem into two subproblems by setting 
(x + 2.625) equal to 1.77218086 and -1.77218086.


Subproblem 1
x + 2.625 = 1.77218086

Simplifying
x + 2.625 = 1.77218086

Reorder the terms:
2.625 + x = 1.77218086

Solving
2.625 + x = 1.77218086

Solving for variable 'x'.

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

Add '-2.625' to each side of the equation.
2.625 + -2.625 + x = 1.77218086 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + x = 1.77218086 + -2.625
x = 1.77218086 + -2.625

Combine like terms: 1.77218086 + -2.625 = -0.85281914
x = -0.85281914

Simplifying
x = -0.85281914


Subproblem 2
x + 2.625 = -1.77218086

Simplifying
x + 2.625 = -1.77218086

Reorder the terms:
2.625 + x = -1.77218086

Solving
2.625 + x = -1.77218086

Solving for variable 'x'.

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

Add '-2.625' to each side of the equation.
2.625 + -2.625 + x = -1.77218086 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + x = -1.77218086 + -2.625
x = -1.77218086 + -2.625

Combine like terms: -1.77218086 + -2.625 = -4.39718086
x = -4.39718086

Simplifying
x = -4.39718086


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.85281914, -4.39718086}

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