x^2-16x=5

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


Simplifying
x2 + -16x = 5

Reorder the terms:
-16x + x2 = 5

Solving
-16x + x2 = 5

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -16x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -16x + x2 = 0 + 5

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

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

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 = 5 + 64

Reorder the terms:
64 + -16x + x2 = 5 + 64

Combine like terms: 5 + 64 = 69
64 + -16x + x2 = 69

Factor a perfect square on the left side:
(x + -8)(x + -8) = 69

Calculate the square root of the right side: 8.306623863

Break this problem into two subproblems by setting 
(x + -8) equal to 8.306623863 and -8.306623863.

Subproblem 1

x + -8 = 8.306623863 Simplifying x + -8 = 8.306623863 Reorder the terms: -8 + x = 8.306623863 Solving -8 + x = 8.306623863 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 = 8.306623863 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.306623863 + 8 x = 8.306623863 + 8 Combine like terms: 8.306623863 + 8 = 16.306623863 x = 16.306623863 Simplifying x = 16.306623863

Subproblem 2

x + -8 = -8.306623863 Simplifying x + -8 = -8.306623863 Reorder the terms: -8 + x = -8.306623863 Solving -8 + x = -8.306623863 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 = -8.306623863 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.306623863 + 8 x = -8.306623863 + 8 Combine like terms: -8.306623863 + 8 = -0.306623863 x = -0.306623863 Simplifying x = -0.306623863

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.306623863, -0.306623863}

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