7x+13x-30-4x^2=0

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Solution for 7x+13x-30-4x^2=0 equation: 


Simplifying
7x + 13x + -30 + -4x2 = 0

Reorder the terms:
-30 + 7x + 13x + -4x2 = 0

Combine like terms: 7x + 13x = 20x
-30 + 20x + -4x2 = 0

Solving
-30 + 20x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 10x + -2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + 10x + -2x2)' equal to zero and attempt to solve:

Simplifying
-15 + 10x + -2x2 = 0

Solving
-15 + 10x + -2x2 = 0

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

Divide each side by '-2'.
7.5 + -5x + x2 = 0

Move the constant term to the right:

Add '-7.5' to each side of the equation.
7.5 + -5x + -7.5 + x2 = 0 + -7.5

Reorder the terms:
7.5 + -7.5 + -5x + x2 = 0 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + -5x + x2 = 0 + -7.5
-5x + x2 = 0 + -7.5

Combine like terms: 0 + -7.5 = -7.5
-5x + x2 = -7.5

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 = -7.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -7.5 + 6.25

Combine like terms: -7.5 + 6.25 = -1.25
6.25 + -5x + x2 = -1.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = -1.25

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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