2x^2=6x-16

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Solution for 2x^2=6x-16 equation: 


Simplifying
2x2 = 6x + -16

Reorder the terms:
2x2 = -16 + 6x

Solving
2x2 = -16 + 6x

Solving for variable 'x'.

Reorder the terms:
16 + -6x + 2x2 = -16 + 6x + 16 + -6x

Reorder the terms:
16 + -6x + 2x2 = -16 + 16 + 6x + -6x

Combine like terms: -16 + 16 = 0
16 + -6x + 2x2 = 0 + 6x + -6x
16 + -6x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
16 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
8 + -3x + x2 = 0

Solving
8 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -3x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -3x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x + x2 = 0 + -8
-3x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-3x + x2 = -8

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -8 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -8 + 2.25

Combine like terms: -8 + 2.25 = -5.75
2.25 + -3x + x2 = -5.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -5.75

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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