x^2+16x+64=32

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Solution for x^2+16x+64=32 equation:


Simplifying
x2 + 16x + 64 = 32

Reorder the terms:
64 + 16x + x2 = 32

Solving
64 + 16x + x2 = 32

Solving for variable 'x'.

Reorder the terms:
64 + -32 + 16x + x2 = 32 + -32

Combine like terms: 64 + -32 = 32
32 + 16x + x2 = 32 + -32

Combine like terms: 32 + -32 = 0
32 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + 16x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + 16x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + 16x + x2 = 0 + -32
16x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
16x + x2 = -32

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 = -32 + 64

Reorder the terms:
64 + 16x + x2 = -32 + 64

Combine like terms: -32 + 64 = 32
64 + 16x + x2 = 32

Factor a perfect square on the left side:
(x + 8)(x + 8) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + 8) equal to 5.656854249 and -5.656854249.

Subproblem 1

x + 8 = 5.656854249 Simplifying x + 8 = 5.656854249 Reorder the terms: 8 + x = 5.656854249 Solving 8 + x = 5.656854249 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 = 5.656854249 + -8 Combine like terms: 8 + -8 = 0 0 + x = 5.656854249 + -8 x = 5.656854249 + -8 Combine like terms: 5.656854249 + -8 = -2.343145751 x = -2.343145751 Simplifying x = -2.343145751

Subproblem 2

x + 8 = -5.656854249 Simplifying x + 8 = -5.656854249 Reorder the terms: 8 + x = -5.656854249 Solving 8 + x = -5.656854249 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 = -5.656854249 + -8 Combine like terms: 8 + -8 = 0 0 + x = -5.656854249 + -8 x = -5.656854249 + -8 Combine like terms: -5.656854249 + -8 = -13.656854249 x = -13.656854249 Simplifying x = -13.656854249

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.343145751, -13.656854249}

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