(x-2)(x-3)=14

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Solution for (x-2)(x-3)=14 equation:


Simplifying
(x + -2)(x + -3) = 14

Reorder the terms:
(-2 + x)(x + -3) = 14

Reorder the terms:
(-2 + x)(-3 + x) = 14

Multiply (-2 + x) * (-3 + x)
(-2(-3 + x) + x(-3 + x)) = 14
((-3 * -2 + x * -2) + x(-3 + x)) = 14
((6 + -2x) + x(-3 + x)) = 14
(6 + -2x + (-3 * x + x * x)) = 14
(6 + -2x + (-3x + x2)) = 14

Combine like terms: -2x + -3x = -5x
(6 + -5x + x2) = 14

Solving
6 + -5x + x2 = 14

Solving for variable 'x'.

Reorder the terms:
6 + -14 + -5x + x2 = 14 + -14

Combine like terms: 6 + -14 = -8
-8 + -5x + x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-8 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -5x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -5x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5x + x2 = 0 + 8
-5x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-5x + x2 = 8

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 8 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 8 + 6.25

Combine like terms: 8 + 6.25 = 14.25
6.25 + -5x + x2 = 14.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

x + -2.5 = 3.774917218 Simplifying x + -2.5 = 3.774917218 Reorder the terms: -2.5 + x = 3.774917218 Solving -2.5 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.774917218 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.774917218 + 2.5 x = 3.774917218 + 2.5 Combine like terms: 3.774917218 + 2.5 = 6.274917218 x = 6.274917218 Simplifying x = 6.274917218

Subproblem 2

x + -2.5 = -3.774917218 Simplifying x + -2.5 = -3.774917218 Reorder the terms: -2.5 + x = -3.774917218 Solving -2.5 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.774917218 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.774917218 + 2.5 x = -3.774917218 + 2.5 Combine like terms: -3.774917218 + 2.5 = -1.274917218 x = -1.274917218 Simplifying x = -1.274917218

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.274917218, -1.274917218}

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