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

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


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

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

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

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

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

Solving
8 + -6x + x2 = 4x

Solving for variable 'x'.

Reorder the terms:
8 + -6x + -4x + x2 = 4x + -4x

Combine like terms: -6x + -4x = -10x
8 + -10x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
8 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -10x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -10x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -10x + x2 = 0 + -8
-10x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-10x + x2 = -8

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -8 + 25

Reorder the terms:
25 + -10x + x2 = -8 + 25

Combine like terms: -8 + 25 = 17
25 + -10x + x2 = 17

Factor a perfect square on the left side:
(x + -5)(x + -5) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + -5) equal to 4.123105626 and -4.123105626.

Subproblem 1

x + -5 = 4.123105626 Simplifying x + -5 = 4.123105626 Reorder the terms: -5 + x = 4.123105626 Solving -5 + x = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.123105626 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.123105626 + 5 x = 4.123105626 + 5 Combine like terms: 4.123105626 + 5 = 9.123105626 x = 9.123105626 Simplifying x = 9.123105626

Subproblem 2

x + -5 = -4.123105626 Simplifying x + -5 = -4.123105626 Reorder the terms: -5 + x = -4.123105626 Solving -5 + x = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.123105626 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.123105626 + 5 x = -4.123105626 + 5 Combine like terms: -4.123105626 + 5 = 0.876894374 x = 0.876894374 Simplifying x = 0.876894374

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.123105626, 0.876894374}

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