8x^2=12x-8

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Solution for 8x^2=12x-8 equation: 


Simplifying
8x2 = 12x + -8

Reorder the terms:
8x2 = -8 + 12x

Solving
8x2 = -8 + 12x

Solving for variable 'x'.

Reorder the terms:
8 + -12x + 8x2 = -8 + 12x + 8 + -12x

Reorder the terms:
8 + -12x + 8x2 = -8 + 8 + 12x + -12x

Combine like terms: -8 + 8 = 0
8 + -12x + 8x2 = 0 + 12x + -12x
8 + -12x + 8x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
8 + -12x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + -3x + 2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(2 + -3x + 2x2)' equal to zero and attempt to solve:

Simplifying
2 + -3x + 2x2 = 0

Solving
2 + -3x + 2x2 = 0

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

Divide each side by '2'.
1 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -1.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1.5x + x2 = 0 + -1
-1.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1.5x + x2 = -1

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 = -1 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -1 + 0.5625

Combine like terms: -1 + 0.5625 = -0.4375
0.5625 + -1.5x + x2 = -0.4375

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