x^2+16x=16

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Solution for x^2+16x=16 equation:


Simplifying
x2 + 16x = 16

Reorder the terms:
16x + x2 = 16

Solving
16x + x2 = 16

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 16 + 64

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

Combine like terms: 16 + 64 = 80
64 + 16x + x2 = 80

Factor a perfect square on the left side:
(x + 8)(x + 8) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(x + 8) equal to 8.94427191 and -8.94427191.

Subproblem 1

x + 8 = 8.94427191 Simplifying x + 8 = 8.94427191 Reorder the terms: 8 + x = 8.94427191 Solving 8 + x = 8.94427191 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 = 8.94427191 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.94427191 + -8 x = 8.94427191 + -8 Combine like terms: 8.94427191 + -8 = 0.94427191 x = 0.94427191 Simplifying x = 0.94427191

Subproblem 2

x + 8 = -8.94427191 Simplifying x + 8 = -8.94427191 Reorder the terms: 8 + x = -8.94427191 Solving 8 + x = -8.94427191 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 = -8.94427191 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.94427191 + -8 x = -8.94427191 + -8 Combine like terms: -8.94427191 + -8 = -16.94427191 x = -16.94427191 Simplifying x = -16.94427191

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.94427191, -16.94427191}

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