(x-2)(x-3)+25=(x+1)-12

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Solution for (x-2)(x-3)+25=(x+1)-12 equation:


Simplifying
(x + -2)(x + -3) + 25 = (x + 1) + -12

Reorder the terms:
(-2 + x)(x + -3) + 25 = (x + 1) + -12

Reorder the terms:
(-2 + x)(-3 + x) + 25 = (x + 1) + -12

Multiply (-2 + x) * (-3 + x)
(-2(-3 + x) + x(-3 + x)) + 25 = (x + 1) + -12
((-3 * -2 + x * -2) + x(-3 + x)) + 25 = (x + 1) + -12
((6 + -2x) + x(-3 + x)) + 25 = (x + 1) + -12
(6 + -2x + (-3 * x + x * x)) + 25 = (x + 1) + -12
(6 + -2x + (-3x + x2)) + 25 = (x + 1) + -12

Combine like terms: -2x + -3x = -5x
(6 + -5x + x2) + 25 = (x + 1) + -12

Reorder the terms:
6 + 25 + -5x + x2 = (x + 1) + -12

Combine like terms: 6 + 25 = 31
31 + -5x + x2 = (x + 1) + -12

Reorder the terms:
31 + -5x + x2 = (1 + x) + -12

Remove parenthesis around (1 + x)
31 + -5x + x2 = 1 + x + -12

Reorder the terms:
31 + -5x + x2 = 1 + -12 + x

Combine like terms: 1 + -12 = -11
31 + -5x + x2 = -11 + x

Solving
31 + -5x + x2 = -11 + x

Solving for variable 'x'.

Reorder the terms:
31 + 11 + -5x + -1x + x2 = -11 + x + 11 + -1x

Combine like terms: 31 + 11 = 42
42 + -5x + -1x + x2 = -11 + x + 11 + -1x

Combine like terms: -5x + -1x = -6x
42 + -6x + x2 = -11 + x + 11 + -1x

Reorder the terms:
42 + -6x + x2 = -11 + 11 + x + -1x

Combine like terms: -11 + 11 = 0
42 + -6x + x2 = 0 + x + -1x
42 + -6x + x2 = x + -1x

Combine like terms: x + -1x = 0
42 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + -6x + -42 + x2 = 0 + -42

Reorder the terms:
42 + -42 + -6x + x2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -6x + x2 = 0 + -42
-6x + x2 = 0 + -42

Combine like terms: 0 + -42 = -42
-6x + x2 = -42

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -42 + 9

Reorder the terms:
9 + -6x + x2 = -42 + 9

Combine like terms: -42 + 9 = -33
9 + -6x + x2 = -33

Factor a perfect square on the left side:
(x + -3)(x + -3) = -33

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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