3x^2+15x+7=0

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Solution for 3x^2+15x+7=0 equation: 


Simplifying
3x2 + 15x + 7 = 0

Reorder the terms:
7 + 15x + 3x2 = 0

Solving
7 + 15x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
2.333333333 + 5x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + 5x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + 5x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + 5x + x2 = 0 + -2.333333333
5x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
5x + x2 = -2.333333333

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -2.333333333 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -2.333333333 + 6.25

Combine like terms: -2.333333333 + 6.25 = 3.916666667
6.25 + 5x + x2 = 3.916666667

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 3.916666667

Calculate the square root of the right side: 1.979057015

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.979057015 and -1.979057015.


Subproblem 1
x + 2.5 = 1.979057015

Simplifying
x + 2.5 = 1.979057015

Reorder the terms:
2.5 + x = 1.979057015

Solving
2.5 + x = 1.979057015

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 1.979057015 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 1.979057015 + -2.5
x = 1.979057015 + -2.5

Combine like terms: 1.979057015 + -2.5 = -0.520942985
x = -0.520942985

Simplifying
x = -0.520942985


Subproblem 2
x + 2.5 = -1.979057015

Simplifying
x + 2.5 = -1.979057015

Reorder the terms:
2.5 + x = -1.979057015

Solving
2.5 + x = -1.979057015

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -1.979057015 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -1.979057015 + -2.5
x = -1.979057015 + -2.5

Combine like terms: -1.979057015 + -2.5 = -4.479057015
x = -4.479057015

Simplifying
x = -4.479057015


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.520942985, -4.479057015}

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