(x-2)(x-3)=12+x*2+8

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Solution for (x-2)(x-3)=12+x*2+8 equation:


Simplifying
(x + -2)(x + -3) = 12 + x * 2 + 8

Reorder the terms:
(-2 + x)(x + -3) = 12 + x * 2 + 8

Reorder the terms:
(-2 + x)(-3 + x) = 12 + x * 2 + 8

Multiply (-2 + x) * (-3 + x)
(-2(-3 + x) + x(-3 + x)) = 12 + x * 2 + 8
((-3 * -2 + x * -2) + x(-3 + x)) = 12 + x * 2 + 8
((6 + -2x) + x(-3 + x)) = 12 + x * 2 + 8
(6 + -2x + (-3 * x + x * x)) = 12 + x * 2 + 8
(6 + -2x + (-3x + x2)) = 12 + x * 2 + 8

Combine like terms: -2x + -3x = -5x
(6 + -5x + x2) = 12 + x * 2 + 8

Reorder the terms for easier multiplication:
6 + -5x + x2 = 12 + 2x + 8

Reorder the terms:
6 + -5x + x2 = 12 + 8 + 2x

Combine like terms: 12 + 8 = 20
6 + -5x + x2 = 20 + 2x

Solving
6 + -5x + x2 = 20 + 2x

Solving for variable 'x'.

Reorder the terms:
6 + -20 + -5x + -2x + x2 = 20 + 2x + -20 + -2x

Combine like terms: 6 + -20 = -14
-14 + -5x + -2x + x2 = 20 + 2x + -20 + -2x

Combine like terms: -5x + -2x = -7x
-14 + -7x + x2 = 20 + 2x + -20 + -2x

Reorder the terms:
-14 + -7x + x2 = 20 + -20 + 2x + -2x

Combine like terms: 20 + -20 = 0
-14 + -7x + x2 = 0 + 2x + -2x
-14 + -7x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-14 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -7x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -7x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -7x + x2 = 0 + 14
-7x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-7x + x2 = 14

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 14 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 14 + 12.25

Combine like terms: 14 + 12.25 = 26.25
12.25 + -7x + x2 = 26.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(x + -3.5) equal to 5.123475383 and -5.123475383.

Subproblem 1

x + -3.5 = 5.123475383 Simplifying x + -3.5 = 5.123475383 Reorder the terms: -3.5 + x = 5.123475383 Solving -3.5 + x = 5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 5.123475383 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.123475383 + 3.5 x = 5.123475383 + 3.5 Combine like terms: 5.123475383 + 3.5 = 8.623475383 x = 8.623475383 Simplifying x = 8.623475383

Subproblem 2

x + -3.5 = -5.123475383 Simplifying x + -3.5 = -5.123475383 Reorder the terms: -3.5 + x = -5.123475383 Solving -3.5 + x = -5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -5.123475383 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.123475383 + 3.5 x = -5.123475383 + 3.5 Combine like terms: -5.123475383 + 3.5 = -1.623475383 x = -1.623475383 Simplifying x = -1.623475383

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.623475383, -1.623475383}

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