(x-2)(x-4)=9x

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Solution for (x-2)(x-4)=9x equation:


Simplifying
(x + -2)(x + -4) = 9x

Reorder the terms:
(-2 + x)(x + -4) = 9x

Reorder the terms:
(-2 + x)(-4 + x) = 9x

Multiply (-2 + x) * (-4 + x)
(-2(-4 + x) + x(-4 + x)) = 9x
((-4 * -2 + x * -2) + x(-4 + x)) = 9x
((8 + -2x) + x(-4 + x)) = 9x
(8 + -2x + (-4 * x + x * x)) = 9x
(8 + -2x + (-4x + x2)) = 9x

Combine like terms: -2x + -4x = -6x
(8 + -6x + x2) = 9x

Solving
8 + -6x + x2 = 9x

Solving for variable 'x'.

Reorder the terms:
8 + -6x + -9x + x2 = 9x + -9x

Combine like terms: -6x + -9x = -15x
8 + -15x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
8 + -15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -15x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -15x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -15x + x2 = 0 + -8
-15x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-15x + x2 = -8

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = -8 + 56.25

Reorder the terms:
56.25 + -15x + x2 = -8 + 56.25

Combine like terms: -8 + 56.25 = 48.25
56.25 + -15x + x2 = 48.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(x + -7.5) equal to 6.946221995 and -6.946221995.

Subproblem 1

x + -7.5 = 6.946221995 Simplifying x + -7.5 = 6.946221995 Reorder the terms: -7.5 + x = 6.946221995 Solving -7.5 + x = 6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 6.946221995 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.946221995 + 7.5 x = 6.946221995 + 7.5 Combine like terms: 6.946221995 + 7.5 = 14.446221995 x = 14.446221995 Simplifying x = 14.446221995

Subproblem 2

x + -7.5 = -6.946221995 Simplifying x + -7.5 = -6.946221995 Reorder the terms: -7.5 + x = -6.946221995 Solving -7.5 + x = -6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -6.946221995 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.946221995 + 7.5 x = -6.946221995 + 7.5 Combine like terms: -6.946221995 + 7.5 = 0.553778005 x = 0.553778005 Simplifying x = 0.553778005

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.446221995, 0.553778005}

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