(8-x)(16-x)=82

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Solution for (8-x)(16-x)=82 equation:


Simplifying
(8 + -1x)(16 + -1x) = 82

Multiply (8 + -1x) * (16 + -1x)
(8(16 + -1x) + -1x * (16 + -1x)) = 82
((16 * 8 + -1x * 8) + -1x * (16 + -1x)) = 82
((128 + -8x) + -1x * (16 + -1x)) = 82
(128 + -8x + (16 * -1x + -1x * -1x)) = 82
(128 + -8x + (-16x + 1x2)) = 82

Combine like terms: -8x + -16x = -24x
(128 + -24x + 1x2) = 82

Solving
128 + -24x + 1x2 = 82

Solving for variable 'x'.

Reorder the terms:
128 + -82 + -24x + 1x2 = 82 + -82

Combine like terms: 128 + -82 = 46
46 + -24x + 1x2 = 82 + -82

Combine like terms: 82 + -82 = 0
46 + -24x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-46' to each side of the equation.
46 + -24x + -46 + x2 = 0 + -46

Reorder the terms:
46 + -46 + -24x + x2 = 0 + -46

Combine like terms: 46 + -46 = 0
0 + -24x + x2 = 0 + -46
-24x + x2 = 0 + -46

Combine like terms: 0 + -46 = -46
-24x + x2 = -46

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -46 + 144

Reorder the terms:
144 + -24x + x2 = -46 + 144

Combine like terms: -46 + 144 = 98
144 + -24x + x2 = 98

Factor a perfect square on the left side:
(x + -12)(x + -12) = 98

Calculate the square root of the right side: 9.899494937

Break this problem into two subproblems by setting 
(x + -12) equal to 9.899494937 and -9.899494937.

Subproblem 1

x + -12 = 9.899494937 Simplifying x + -12 = 9.899494937 Reorder the terms: -12 + x = 9.899494937 Solving -12 + x = 9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 9.899494937 + 12 Combine like terms: -12 + 12 = 0 0 + x = 9.899494937 + 12 x = 9.899494937 + 12 Combine like terms: 9.899494937 + 12 = 21.899494937 x = 21.899494937 Simplifying x = 21.899494937

Subproblem 2

x + -12 = -9.899494937 Simplifying x + -12 = -9.899494937 Reorder the terms: -12 + x = -9.899494937 Solving -12 + x = -9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -9.899494937 + 12 Combine like terms: -12 + 12 = 0 0 + x = -9.899494937 + 12 x = -9.899494937 + 12 Combine like terms: -9.899494937 + 12 = 2.100505063 x = 2.100505063 Simplifying x = 2.100505063

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21.899494937, 2.100505063}

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