x(-4x-13)=14

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Solution for x(-4x-13)=14 equation: 


Simplifying
x(-4x + -13) = 14

Reorder the terms:
x(-13 + -4x) = 14
(-13 * x + -4x * x) = 14
(-13x + -4x2) = 14

Solving
-13x + -4x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + -13x + -4x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + -13x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 13x + 4x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(14 + 13x + 4x2)' equal to zero and attempt to solve:

Simplifying
14 + 13x + 4x2 = 0

Solving
14 + 13x + 4x2 = 0

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

Divide each side by '4'.
3.5 + 3.25x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 3.25x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 3.25x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 3.25x + x2 = 0 + -3.5
3.25x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
3.25x + x2 = -3.5

The x term is 3.25x.  Take half its coefficient (1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
3.25x + 2.640625 + x2 = -3.5 + 2.640625

Reorder the terms:
2.640625 + 3.25x + x2 = -3.5 + 2.640625

Combine like terms: -3.5 + 2.640625 = -0.859375
2.640625 + 3.25x + x2 = -0.859375

Factor a perfect square on the left side:
(x + 1.625)(x + 1.625) = -0.859375

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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