(2x-3)=(x^2-3x+5)

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Solution for (2x-3)=(x^2-3x+5) equation: 


Simplifying
(2x + -3) = (x2 + -3x + 5)

Reorder the terms:
(-3 + 2x) = (x2 + -3x + 5)

Remove parenthesis around (-3 + 2x)
-3 + 2x = (x2 + -3x + 5)

Reorder the terms:
-3 + 2x = (5 + -3x + x2)

Remove parenthesis around (5 + -3x + x2)
-3 + 2x = 5 + -3x + x2

Solving
-3 + 2x = 5 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
-3 + -5 + 2x + 3x + -1x2 = 5 + -3x + x2 + -5 + 3x + -1x2

Combine like terms: -3 + -5 = -8
-8 + 2x + 3x + -1x2 = 5 + -3x + x2 + -5 + 3x + -1x2

Combine like terms: 2x + 3x = 5x
-8 + 5x + -1x2 = 5 + -3x + x2 + -5 + 3x + -1x2

Reorder the terms:
-8 + 5x + -1x2 = 5 + -5 + -3x + 3x + x2 + -1x2

Combine like terms: 5 + -5 = 0
-8 + 5x + -1x2 = 0 + -3x + 3x + x2 + -1x2
-8 + 5x + -1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
-8 + 5x + -1x2 = 0 + x2 + -1x2
-8 + 5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + 5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
8 + -5x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -5x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -5x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x + x2 = 0 + -8
-5x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-5x + x2 = -8

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 = -8 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -8 + 6.25

Combine like terms: -8 + 6.25 = -1.75
6.25 + -5x + x2 = -1.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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