2x^2-9x=x-20

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Solution for 2x^2-9x=x-20 equation: 


Simplifying
2x2 + -9x = x + -20

Reorder the terms:
-9x + 2x2 = x + -20

Reorder the terms:
-9x + 2x2 = -20 + x

Solving
-9x + 2x2 = -20 + x

Solving for variable 'x'.

Reorder the terms:
20 + -9x + -1x + 2x2 = -20 + x + 20 + -1x

Combine like terms: -9x + -1x = -10x
20 + -10x + 2x2 = -20 + x + 20 + -1x

Reorder the terms:
20 + -10x + 2x2 = -20 + 20 + x + -1x

Combine like terms: -20 + 20 = 0
20 + -10x + 2x2 = 0 + x + -1x
20 + -10x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
20 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(10 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
10 + -5x + x2 = 0

Solving
10 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -5x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -5x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -5x + x2 = 0 + -10
-5x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-5x + x2 = -10

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -10 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -10 + 6.25

Combine like terms: -10 + 6.25 = -3.75
6.25 + -5x + x2 = -3.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = -3.75

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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