x^2-3x=2x^2+7

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Solution for x^2-3x=2x^2+7 equation:


Simplifying
x2 + -3x = 2x2 + 7

Reorder the terms:
-3x + x2 = 2x2 + 7

Reorder the terms:
-3x + x2 = 7 + 2x2

Solving
-3x + x2 = 7 + 2x2

Solving for variable 'x'.

Reorder the terms:
-7 + -3x + x2 + -2x2 = 7 + 2x2 + -7 + -2x2

Combine like terms: x2 + -2x2 = -1x2
-7 + -3x + -1x2 = 7 + 2x2 + -7 + -2x2

Reorder the terms:
-7 + -3x + -1x2 = 7 + -7 + 2x2 + -2x2

Combine like terms: 7 + -7 = 0
-7 + -3x + -1x2 = 0 + 2x2 + -2x2
-7 + -3x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-7 + -3x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 3x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
7 + 3x + x2 = 0

Solving
7 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 3x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 3x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x + x2 = 0 + -7
3x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
3x + x2 = -7

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 = -7 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -7 + 2.25

Combine like terms: -7 + 2.25 = -4.75
2.25 + 3x + x2 = -4.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -4.75

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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