13=3(x-1)(x-8)

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Solution for 13=3(x-1)(x-8) equation:


Simplifying
13 = 3(x + -1)(x + -8)

Reorder the terms:
13 = 3(-1 + x)(x + -8)

Reorder the terms:
13 = 3(-1 + x)(-8 + x)

Multiply (-1 + x) * (-8 + x)
13 = 3(-1(-8 + x) + x(-8 + x))
13 = 3((-8 * -1 + x * -1) + x(-8 + x))
13 = 3((8 + -1x) + x(-8 + x))
13 = 3(8 + -1x + (-8 * x + x * x))
13 = 3(8 + -1x + (-8x + x2))

Combine like terms: -1x + -8x = -9x
13 = 3(8 + -9x + x2)
13 = (8 * 3 + -9x * 3 + x2 * 3)
13 = (24 + -27x + 3x2)

Solving
13 = 24 + -27x + 3x2

Solving for variable 'x'.

Combine like terms: 13 + -24 = -11
-11 + 27x + -3x2 = 24 + -27x + 3x2 + -24 + 27x + -3x2

Reorder the terms:
-11 + 27x + -3x2 = 24 + -24 + -27x + 27x + 3x2 + -3x2

Combine like terms: 24 + -24 = 0
-11 + 27x + -3x2 = 0 + -27x + 27x + 3x2 + -3x2
-11 + 27x + -3x2 = -27x + 27x + 3x2 + -3x2

Combine like terms: -27x + 27x = 0
-11 + 27x + -3x2 = 0 + 3x2 + -3x2
-11 + 27x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-11 + 27x + -3x2 = 0

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

Divide each side by '-3'.
3.666666667 + -9x + x2 = 0

Move the constant term to the right:

Add '-3.666666667' to each side of the equation.
3.666666667 + -9x + -3.666666667 + x2 = 0 + -3.666666667

Reorder the terms:
3.666666667 + -3.666666667 + -9x + x2 = 0 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + -9x + x2 = 0 + -3.666666667
-9x + x2 = 0 + -3.666666667

Combine like terms: 0 + -3.666666667 = -3.666666667
-9x + x2 = -3.666666667

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -3.666666667 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -3.666666667 + 20.25

Combine like terms: -3.666666667 + 20.25 = 16.583333333
20.25 + -9x + x2 = 16.583333333

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 16.583333333

Calculate the square root of the right side: 4.072263908

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.072263908 and -4.072263908.

Subproblem 1

x + -4.5 = 4.072263908 Simplifying x + -4.5 = 4.072263908 Reorder the terms: -4.5 + x = 4.072263908 Solving -4.5 + x = 4.072263908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.072263908 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.072263908 + 4.5 x = 4.072263908 + 4.5 Combine like terms: 4.072263908 + 4.5 = 8.572263908 x = 8.572263908 Simplifying x = 8.572263908

Subproblem 2

x + -4.5 = -4.072263908 Simplifying x + -4.5 = -4.072263908 Reorder the terms: -4.5 + x = -4.072263908 Solving -4.5 + x = -4.072263908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.072263908 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.072263908 + 4.5 x = -4.072263908 + 4.5 Combine like terms: -4.072263908 + 4.5 = 0.427736092 x = 0.427736092 Simplifying x = 0.427736092

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.572263908, 0.427736092}

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