-16x^2+24x-8=68

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Solution for -16x^2+24x-8=68 equation: 


Simplifying
-16x2 + 24x + -8 = 68

Reorder the terms:
-8 + 24x + -16x2 = 68

Solving
-8 + 24x + -16x2 = 68

Solving for variable 'x'.

Reorder the terms:
-8 + -68 + 24x + -16x2 = 68 + -68

Combine like terms: -8 + -68 = -76
-76 + 24x + -16x2 = 68 + -68

Combine like terms: 68 + -68 = 0
-76 + 24x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-19 + 6x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-19 + 6x + -4x2)' equal to zero and attempt to solve:

Simplifying
-19 + 6x + -4x2 = 0

Solving
-19 + 6x + -4x2 = 0

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

Divide each side by '-4'.
4.75 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-4.75' to each side of the equation.
4.75 + -1.5x + -4.75 + x2 = 0 + -4.75

Reorder the terms:
4.75 + -4.75 + -1.5x + x2 = 0 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + -1.5x + x2 = 0 + -4.75
-1.5x + x2 = 0 + -4.75

Combine like terms: 0 + -4.75 = -4.75
-1.5x + x2 = -4.75

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -4.75 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -4.75 + 0.5625

Combine like terms: -4.75 + 0.5625 = -4.1875
0.5625 + -1.5x + x2 = -4.1875

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = -4.1875

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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