x^2-16x-60=0

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Solution for x^2-16x-60=0 equation:


Simplifying
x2 + -16x + -60 = 0

Reorder the terms:
-60 + -16x + x2 = 0

Solving
-60 + -16x + 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 + -16x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + -16x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -16x + x2 = 0 + 60
-16x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
-16x + x2 = 60

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 60 + 64

Reorder the terms:
64 + -16x + x2 = 60 + 64

Combine like terms: 60 + 64 = 124
64 + -16x + x2 = 124

Factor a perfect square on the left side:
(x + -8)(x + -8) = 124

Calculate the square root of the right side: 11.135528726

Break this problem into two subproblems by setting 
(x + -8) equal to 11.135528726 and -11.135528726.

Subproblem 1

x + -8 = 11.135528726 Simplifying x + -8 = 11.135528726 Reorder the terms: -8 + x = 11.135528726 Solving -8 + x = 11.135528726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 11.135528726 + 8 Combine like terms: -8 + 8 = 0 0 + x = 11.135528726 + 8 x = 11.135528726 + 8 Combine like terms: 11.135528726 + 8 = 19.135528726 x = 19.135528726 Simplifying x = 19.135528726

Subproblem 2

x + -8 = -11.135528726 Simplifying x + -8 = -11.135528726 Reorder the terms: -8 + x = -11.135528726 Solving -8 + x = -11.135528726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -11.135528726 + 8 Combine like terms: -8 + 8 = 0 0 + x = -11.135528726 + 8 x = -11.135528726 + 8 Combine like terms: -11.135528726 + 8 = -3.135528726 x = -3.135528726 Simplifying x = -3.135528726

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.135528726, -3.135528726}

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