(x-4)(3x-10)=(x-2)+18

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Solution for (x-4)(3x-10)=(x-2)+18 equation:


Simplifying
(x + -4)(3x + -10) = (x + -2) + 18

Reorder the terms:
(-4 + x)(3x + -10) = (x + -2) + 18

Reorder the terms:
(-4 + x)(-10 + 3x) = (x + -2) + 18

Multiply (-4 + x) * (-10 + 3x)
(-4(-10 + 3x) + x(-10 + 3x)) = (x + -2) + 18
((-10 * -4 + 3x * -4) + x(-10 + 3x)) = (x + -2) + 18
((40 + -12x) + x(-10 + 3x)) = (x + -2) + 18
(40 + -12x + (-10 * x + 3x * x)) = (x + -2) + 18
(40 + -12x + (-10x + 3x2)) = (x + -2) + 18

Combine like terms: -12x + -10x = -22x
(40 + -22x + 3x2) = (x + -2) + 18

Reorder the terms:
40 + -22x + 3x2 = (-2 + x) + 18

Remove parenthesis around (-2 + x)
40 + -22x + 3x2 = -2 + x + 18

Reorder the terms:
40 + -22x + 3x2 = -2 + 18 + x

Combine like terms: -2 + 18 = 16
40 + -22x + 3x2 = 16 + x

Solving
40 + -22x + 3x2 = 16 + x

Solving for variable 'x'.

Reorder the terms:
40 + -16 + -22x + -1x + 3x2 = 16 + x + -16 + -1x

Combine like terms: 40 + -16 = 24
24 + -22x + -1x + 3x2 = 16 + x + -16 + -1x

Combine like terms: -22x + -1x = -23x
24 + -23x + 3x2 = 16 + x + -16 + -1x

Reorder the terms:
24 + -23x + 3x2 = 16 + -16 + x + -1x

Combine like terms: 16 + -16 = 0
24 + -23x + 3x2 = 0 + x + -1x
24 + -23x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
24 + -23x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
8 + -7.666666667x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -7.666666667x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -7.666666667x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7.666666667x + x2 = 0 + -8
-7.666666667x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-7.666666667x + x2 = -8

The x term is -7.666666667x.  Take half its coefficient (-3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
-7.666666667x + 14.69444445 + x2 = -8 + 14.69444445

Reorder the terms:
14.69444445 + -7.666666667x + x2 = -8 + 14.69444445

Combine like terms: -8 + 14.69444445 = 6.69444445
14.69444445 + -7.666666667x + x2 = 6.69444445

Factor a perfect square on the left side:
(x + -3.833333334)(x + -3.833333334) = 6.69444445

Calculate the square root of the right side: 2.58736245

Break this problem into two subproblems by setting 
(x + -3.833333334) equal to 2.58736245 and -2.58736245.

Subproblem 1

x + -3.833333334 = 2.58736245 Simplifying x + -3.833333334 = 2.58736245 Reorder the terms: -3.833333334 + x = 2.58736245 Solving -3.833333334 + x = 2.58736245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 2.58736245 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 2.58736245 + 3.833333334 x = 2.58736245 + 3.833333334 Combine like terms: 2.58736245 + 3.833333334 = 6.420695784 x = 6.420695784 Simplifying x = 6.420695784

Subproblem 2

x + -3.833333334 = -2.58736245 Simplifying x + -3.833333334 = -2.58736245 Reorder the terms: -3.833333334 + x = -2.58736245 Solving -3.833333334 + x = -2.58736245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -2.58736245 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -2.58736245 + 3.833333334 x = -2.58736245 + 3.833333334 Combine like terms: -2.58736245 + 3.833333334 = 1.245970884 x = 1.245970884 Simplifying x = 1.245970884

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.420695784, 1.245970884}

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