-8x^2+54x-196=0

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Solution for -8x^2+54x-196=0 equation: 


Simplifying
-8x2 + 54x + -196 = 0

Reorder the terms:
-196 + 54x + -8x2 = 0

Solving
-196 + 54x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-98 + 27x + -4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-98 + 27x + -4x2)' equal to zero and attempt to solve:

Simplifying
-98 + 27x + -4x2 = 0

Solving
-98 + 27x + -4x2 = 0

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

Divide each side by '-4'.
24.5 + -6.75x + x2 = 0

Move the constant term to the right:

Add '-24.5' to each side of the equation.
24.5 + -6.75x + -24.5 + x2 = 0 + -24.5

Reorder the terms:
24.5 + -24.5 + -6.75x + x2 = 0 + -24.5

Combine like terms: 24.5 + -24.5 = 0.0
0.0 + -6.75x + x2 = 0 + -24.5
-6.75x + x2 = 0 + -24.5

Combine like terms: 0 + -24.5 = -24.5
-6.75x + x2 = -24.5

The x term is -6.75x.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75x + 11.390625 + x2 = -24.5 + 11.390625

Reorder the terms:
11.390625 + -6.75x + x2 = -24.5 + 11.390625

Combine like terms: -24.5 + 11.390625 = -13.109375
11.390625 + -6.75x + x2 = -13.109375

Factor a perfect square on the left side:
(x + -3.375)(x + -3.375) = -13.109375

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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