9x^2+30x+25=-14

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Solution for 9x^2+30x+25=-14 equation:


Simplifying
9x2 + 30x + 25 = -14

Reorder the terms:
25 + 30x + 9x2 = -14

Solving
25 + 30x + 9x2 = -14

Solving for variable 'x'.

Reorder the terms:
25 + 14 + 30x + 9x2 = -14 + 14

Combine like terms: 25 + 14 = 39
39 + 30x + 9x2 = -14 + 14

Combine like terms: -14 + 14 = 0
39 + 30x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(13 + 10x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(13 + 10x + 3x2)' equal to zero and attempt to solve:

Simplifying
13 + 10x + 3x2 = 0

Solving
13 + 10x + 3x2 = 0

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

Divide each side by '3'.
4.333333333 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '-4.333333333' to each side of the equation.
4.333333333 + 3.333333333x + -4.333333333 + x2 = 0 + -4.333333333

Reorder the terms:
4.333333333 + -4.333333333 + 3.333333333x + x2 = 0 + -4.333333333

Combine like terms: 4.333333333 + -4.333333333 = 0.000000000
0.000000000 + 3.333333333x + x2 = 0 + -4.333333333
3.333333333x + x2 = 0 + -4.333333333

Combine like terms: 0 + -4.333333333 = -4.333333333
3.333333333x + x2 = -4.333333333

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = -4.333333333 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = -4.333333333 + 2.777777779

Combine like terms: -4.333333333 + 2.777777779 = -1.555555554
2.777777779 + 3.333333333x + x2 = -1.555555554

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = -1.555555554

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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