0=-3x^2-21x-15

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Solution for 0=-3x^2-21x-15 equation: 


Simplifying
0 = -3x2 + -21x + -15

Reorder the terms:
0 = -15 + -21x + -3x2

Solving
0 = -15 + -21x + -3x2

Solving for variable 'x'.

Combine like terms: 0 + 15 = 15
15 + 21x + 3x2 = -15 + -21x + -3x2 + 15 + 21x + 3x2

Reorder the terms:
15 + 21x + 3x2 = -15 + 15 + -21x + 21x + -3x2 + 3x2

Combine like terms: -15 + 15 = 0
15 + 21x + 3x2 = 0 + -21x + 21x + -3x2 + 3x2
15 + 21x + 3x2 = -21x + 21x + -3x2 + 3x2

Combine like terms: -21x + 21x = 0
15 + 21x + 3x2 = 0 + -3x2 + 3x2
15 + 21x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
15 + 21x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 7x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
5 + 7x + x2 = 0

Solving
5 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 7x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 7x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 7x + x2 = 0 + -5
7x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
7x + x2 = -5

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -5 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -5 + 12.25

Combine like terms: -5 + 12.25 = 7.25
12.25 + 7x + x2 = 7.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(x + 3.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
x + 3.5 = 2.692582404

Simplifying
x + 3.5 = 2.692582404

Reorder the terms:
3.5 + x = 2.692582404

Solving
3.5 + x = 2.692582404

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 2.692582404 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 2.692582404 + -3.5
x = 2.692582404 + -3.5

Combine like terms: 2.692582404 + -3.5 = -0.807417596
x = -0.807417596

Simplifying
x = -0.807417596


Subproblem 2
x + 3.5 = -2.692582404

Simplifying
x + 3.5 = -2.692582404

Reorder the terms:
3.5 + x = -2.692582404

Solving
3.5 + x = -2.692582404

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -2.692582404 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -2.692582404 + -3.5
x = -2.692582404 + -3.5

Combine like terms: -2.692582404 + -3.5 = -6.192582404
x = -6.192582404

Simplifying
x = -6.192582404


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.807417596, -6.192582404}
Solution
x = {-0.807417596, -6.192582404}

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