x(x-2)-60=0

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Solution for x(x-2)-60=0 equation:


Simplifying
x(x + -2) + -60 = 0

Reorder the terms:
x(-2 + x) + -60 = 0
(-2 * x + x * x) + -60 = 0
(-2x + x2) + -60 = 0

Reorder the terms:
-60 + -2x + x2 = 0

Solving
-60 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -2x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + -2x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -2x + x2 = 0 + 60
-2x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
-2x + x2 = 60

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 = 60 + 1

Reorder the terms:
1 + -2x + x2 = 60 + 1

Combine like terms: 60 + 1 = 61
1 + -2x + x2 = 61

Factor a perfect square on the left side:
(x + -1)(x + -1) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(x + -1) equal to 7.810249676 and -7.810249676.

Subproblem 1

x + -1 = 7.810249676 Simplifying x + -1 = 7.810249676 Reorder the terms: -1 + x = 7.810249676 Solving -1 + x = 7.810249676 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 = 7.810249676 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.810249676 + 1 x = 7.810249676 + 1 Combine like terms: 7.810249676 + 1 = 8.810249676 x = 8.810249676 Simplifying x = 8.810249676

Subproblem 2

x + -1 = -7.810249676 Simplifying x + -1 = -7.810249676 Reorder the terms: -1 + x = -7.810249676 Solving -1 + x = -7.810249676 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 = -7.810249676 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.810249676 + 1 x = -7.810249676 + 1 Combine like terms: -7.810249676 + 1 = -6.810249676 x = -6.810249676 Simplifying x = -6.810249676

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.810249676, -6.810249676}

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