4x^2+30x+58=0

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Solution for 4x^2+30x+58=0 equation: 


Simplifying
4x2 + 30x + 58 = 0

Reorder the terms:
58 + 30x + 4x2 = 0

Solving
58 + 30x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(29 + 15x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(29 + 15x + 2x2)' equal to zero and attempt to solve:

Simplifying
29 + 15x + 2x2 = 0

Solving
29 + 15x + 2x2 = 0

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

Divide each side by '2'.
14.5 + 7.5x + x2 = 0

Move the constant term to the right:

Add '-14.5' to each side of the equation.
14.5 + 7.5x + -14.5 + x2 = 0 + -14.5

Reorder the terms:
14.5 + -14.5 + 7.5x + x2 = 0 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + 7.5x + x2 = 0 + -14.5
7.5x + x2 = 0 + -14.5

Combine like terms: 0 + -14.5 = -14.5
7.5x + x2 = -14.5

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = -14.5 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = -14.5 + 14.0625

Combine like terms: -14.5 + 14.0625 = -0.4375
14.0625 + 7.5x + x2 = -0.4375

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = -0.4375

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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