x^2-16x-32=5

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Solution for x^2-16x-32=5 equation:


Simplifying
x2 + -16x + -32 = 5

Reorder the terms:
-32 + -16x + x2 = 5

Solving
-32 + -16x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
-32 + -5 + -16x + x2 = 5 + -5

Combine like terms: -32 + -5 = -37
-37 + -16x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-37 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + -16x + 37 + x2 = 0 + 37

Reorder the terms:
-37 + 37 + -16x + x2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -16x + x2 = 0 + 37
-16x + x2 = 0 + 37

Combine like terms: 0 + 37 = 37
-16x + x2 = 37

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 = 37 + 64

Reorder the terms:
64 + -16x + x2 = 37 + 64

Combine like terms: 37 + 64 = 101
64 + -16x + x2 = 101

Factor a perfect square on the left side:
(x + -8)(x + -8) = 101

Calculate the square root of the right side: 10.049875621

Break this problem into two subproblems by setting 
(x + -8) equal to 10.049875621 and -10.049875621.

Subproblem 1

x + -8 = 10.049875621 Simplifying x + -8 = 10.049875621 Reorder the terms: -8 + x = 10.049875621 Solving -8 + x = 10.049875621 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 = 10.049875621 + 8 Combine like terms: -8 + 8 = 0 0 + x = 10.049875621 + 8 x = 10.049875621 + 8 Combine like terms: 10.049875621 + 8 = 18.049875621 x = 18.049875621 Simplifying x = 18.049875621

Subproblem 2

x + -8 = -10.049875621 Simplifying x + -8 = -10.049875621 Reorder the terms: -8 + x = -10.049875621 Solving -8 + x = -10.049875621 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 = -10.049875621 + 8 Combine like terms: -8 + 8 = 0 0 + x = -10.049875621 + 8 x = -10.049875621 + 8 Combine like terms: -10.049875621 + 8 = -2.049875621 x = -2.049875621 Simplifying x = -2.049875621

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.049875621, -2.049875621}

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