x(x-6)+x^2=(x-5)(x+2)

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Solution for x(x-6)+x^2=(x-5)(x+2) equation:


Simplifying
x(x + -6) + x2 = (x + -5)(x + 2)

Reorder the terms:
x(-6 + x) + x2 = (x + -5)(x + 2)
(-6 * x + x * x) + x2 = (x + -5)(x + 2)
(-6x + x2) + x2 = (x + -5)(x + 2)

Combine like terms: x2 + x2 = 2x2
-6x + 2x2 = (x + -5)(x + 2)

Reorder the terms:
-6x + 2x2 = (-5 + x)(x + 2)

Reorder the terms:
-6x + 2x2 = (-5 + x)(2 + x)

Multiply (-5 + x) * (2 + x)
-6x + 2x2 = (-5(2 + x) + x(2 + x))
-6x + 2x2 = ((2 * -5 + x * -5) + x(2 + x))
-6x + 2x2 = ((-10 + -5x) + x(2 + x))
-6x + 2x2 = (-10 + -5x + (2 * x + x * x))
-6x + 2x2 = (-10 + -5x + (2x + x2))

Combine like terms: -5x + 2x = -3x
-6x + 2x2 = (-10 + -3x + x2)

Solving
-6x + 2x2 = -10 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
10 + -6x + 3x + 2x2 + -1x2 = -10 + -3x + x2 + 10 + 3x + -1x2

Combine like terms: -6x + 3x = -3x
10 + -3x + 2x2 + -1x2 = -10 + -3x + x2 + 10 + 3x + -1x2

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

Reorder the terms:
10 + -3x + 1x2 = -10 + 10 + -3x + 3x + x2 + -1x2

Combine like terms: -10 + 10 = 0
10 + -3x + 1x2 = 0 + -3x + 3x + x2 + -1x2
10 + -3x + 1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
10 + -3x + 1x2 = 0 + x2 + -1x2
10 + -3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + -3x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -3x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -3x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x + x2 = 0 + -10
-3x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-3x + x2 = -10

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 = -10 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -10 + 2.25

Combine like terms: -10 + 2.25 = -7.75
2.25 + -3x + x2 = -7.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -7.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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