-x^2+32x+16=0

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Solution for -x^2+32x+16=0 equation:


Simplifying
-1x2 + 32x + 16 = 0

Reorder the terms:
16 + 32x + -1x2 = 0

Solving
16 + 32x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-16 + -32x + x2 = 0

Move the constant term to the right:

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

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

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

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

The x term is -32x.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32x + 256 + x2 = 16 + 256

Reorder the terms:
256 + -32x + x2 = 16 + 256

Combine like terms: 16 + 256 = 272
256 + -32x + x2 = 272

Factor a perfect square on the left side:
(x + -16)(x + -16) = 272

Calculate the square root of the right side: 16.492422502

Break this problem into two subproblems by setting 
(x + -16) equal to 16.492422502 and -16.492422502.

Subproblem 1

x + -16 = 16.492422502 Simplifying x + -16 = 16.492422502 Reorder the terms: -16 + x = 16.492422502 Solving -16 + x = 16.492422502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 16.492422502 + 16 Combine like terms: -16 + 16 = 0 0 + x = 16.492422502 + 16 x = 16.492422502 + 16 Combine like terms: 16.492422502 + 16 = 32.492422502 x = 32.492422502 Simplifying x = 32.492422502

Subproblem 2

x + -16 = -16.492422502 Simplifying x + -16 = -16.492422502 Reorder the terms: -16 + x = -16.492422502 Solving -16 + x = -16.492422502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -16.492422502 + 16 Combine like terms: -16 + 16 = 0 0 + x = -16.492422502 + 16 x = -16.492422502 + 16 Combine like terms: -16.492422502 + 16 = -0.492422502 x = -0.492422502 Simplifying x = -0.492422502

Solution

The solution to the problem is based on the solutions from the subproblems. x = {32.492422502, -0.492422502}

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