(2x^2-4x+5)-(-x^2+3x)=0

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Solution for (2x^2-4x+5)-(-x^2+3x)=0 equation: 


Simplifying
(2x2 + -4x + 5) + -1(-1x2 + 3x) = 0

Reorder the terms:
(5 + -4x + 2x2) + -1(-1x2 + 3x) = 0

Remove parenthesis around (5 + -4x + 2x2)
5 + -4x + 2x2 + -1(-1x2 + 3x) = 0

Reorder the terms:
5 + -4x + 2x2 + -1(3x + -1x2) = 0
5 + -4x + 2x2 + (3x * -1 + -1x2 * -1) = 0
5 + -4x + 2x2 + (-3x + 1x2) = 0

Reorder the terms:
5 + -4x + -3x + 2x2 + 1x2 = 0

Combine like terms: -4x + -3x = -7x
5 + -7x + 2x2 + 1x2 = 0

Combine like terms: 2x2 + 1x2 = 3x2
5 + -7x + 3x2 = 0

Solving
5 + -7x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
1.666666667 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -2.333333333x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -2.333333333x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -2.333333333x + x2 = 0 + -1.666666667
-2.333333333x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-2.333333333x + x2 = -1.666666667

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = -1.666666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = -1.666666667 + 1.361111112

Combine like terms: -1.666666667 + 1.361111112 = -0.305555555
1.361111112 + -2.333333333x + x2 = -0.305555555

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = -0.305555555

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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