x(x-1)-(x-5)2=2

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Solution for x(x-1)-(x-5)2=2 equation: 


Simplifying
x(x + -1) + -1(x + -5) * 2 = 2

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

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

Reorder the terms for easier multiplication:
-1x + x2 + -1 * 2(-5 + x) = 2

Multiply -1 * 2
-1x + x2 + -2(-5 + x) = 2
-1x + x2 + (-5 * -2 + x * -2) = 2
-1x + x2 + (10 + -2x) = 2

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

Combine like terms: -1x + -2x = -3x
10 + -3x + x2 = 2

Solving
10 + -3x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
10 + -2 + -3x + x2 = 2 + -2

Combine like terms: 10 + -2 = 8
8 + -3x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
8 + -3x + x2 = 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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