85=x(x-2)

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Solution for 85=x(x-2) equation:


Simplifying
85 = x(x + -2)

Reorder the terms:
85 = x(-2 + x)
85 = (-2 * x + x * x)
85 = (-2x + x2)

Solving
85 = -2x + x2

Solving for variable 'x'.

Reorder the terms:
85 + 2x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
85 + 2x + -1x2 = 0 + x2 + -1x2
85 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
85 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-85 + -2x + x2 = 0

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + -2x + 85 + x2 = 0 + 85

Reorder the terms:
-85 + 85 + -2x + x2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + -2x + x2 = 0 + 85
-2x + x2 = 0 + 85

Combine like terms: 0 + 85 = 85
-2x + x2 = 85

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 85 + 1

Reorder the terms:
1 + -2x + x2 = 85 + 1

Combine like terms: 85 + 1 = 86
1 + -2x + x2 = 86

Factor a perfect square on the left side:
(x + -1)(x + -1) = 86

Calculate the square root of the right side: 9.273618495

Break this problem into two subproblems by setting 
(x + -1) equal to 9.273618495 and -9.273618495.

Subproblem 1

x + -1 = 9.273618495 Simplifying x + -1 = 9.273618495 Reorder the terms: -1 + x = 9.273618495 Solving -1 + x = 9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 9.273618495 + 1 Combine like terms: -1 + 1 = 0 0 + x = 9.273618495 + 1 x = 9.273618495 + 1 Combine like terms: 9.273618495 + 1 = 10.273618495 x = 10.273618495 Simplifying x = 10.273618495

Subproblem 2

x + -1 = -9.273618495 Simplifying x + -1 = -9.273618495 Reorder the terms: -1 + x = -9.273618495 Solving -1 + x = -9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -9.273618495 + 1 Combine like terms: -1 + 1 = 0 0 + x = -9.273618495 + 1 x = -9.273618495 + 1 Combine like terms: -9.273618495 + 1 = -8.273618495 x = -8.273618495 Simplifying x = -8.273618495

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.273618495, -8.273618495}

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