4x^2+14x+30=0

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Solution for 4x^2+14x+30=0 equation: 


Simplifying
4x2 + 14x + 30 = 0

Reorder the terms:
30 + 14x + 4x2 = 0

Solving
30 + 14x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 7x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(15 + 7x + 2x2)' equal to zero and attempt to solve:

Simplifying
15 + 7x + 2x2 = 0

Solving
15 + 7x + 2x2 = 0

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

Divide each side by '2'.
7.5 + 3.5x + x2 = 0

Move the constant term to the right:

Add '-7.5' to each side of the equation.
7.5 + 3.5x + -7.5 + x2 = 0 + -7.5

Reorder the terms:
7.5 + -7.5 + 3.5x + x2 = 0 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + 3.5x + x2 = 0 + -7.5
3.5x + x2 = 0 + -7.5

Combine like terms: 0 + -7.5 = -7.5
3.5x + x2 = -7.5

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = -7.5 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = -7.5 + 3.0625

Combine like terms: -7.5 + 3.0625 = -4.4375
3.0625 + 3.5x + x2 = -4.4375

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = -4.4375

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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