2x^2+3x=2(3x-4)+x^2

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Solution for 2x^2+3x=2(3x-4)+x^2 equation: 


Simplifying
2x2 + 3x = 2(3x + -4) + x2

Reorder the terms:
3x + 2x2 = 2(3x + -4) + x2

Reorder the terms:
3x + 2x2 = 2(-4 + 3x) + x2
3x + 2x2 = (-4 * 2 + 3x * 2) + x2
3x + 2x2 = (-8 + 6x) + x2

Solving
3x + 2x2 = -8 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
8 + 3x + -6x + 2x2 + -1x2 = -8 + 6x + x2 + 8 + -6x + -1x2

Combine like terms: 3x + -6x = -3x
8 + -3x + 2x2 + -1x2 = -8 + 6x + x2 + 8 + -6x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
8 + -3x + 1x2 = -8 + 6x + x2 + 8 + -6x + -1x2

Reorder the terms:
8 + -3x + 1x2 = -8 + 8 + 6x + -6x + x2 + -1x2

Combine like terms: -8 + 8 = 0
8 + -3x + 1x2 = 0 + 6x + -6x + x2 + -1x2
8 + -3x + 1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
8 + -3x + 1x2 = 0 + x2 + -1x2
8 + -3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + -3x + 1x2 = 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.

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