16=2x-.0625x^2

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Solution for 16=2x-.0625x^2 equation:


Simplifying
16 = 2x + -0.0625x2

Solving
16 = 2x + -0.0625x2

Solving for variable 'x'.

Reorder the terms:
16 + -2x + 0.0625x2 = 2x + -2x + -0.0625x2 + 0.0625x2

Combine like terms: 2x + -2x = 0
16 + -2x + 0.0625x2 = 0 + -0.0625x2 + 0.0625x2
16 + -2x + 0.0625x2 = -0.0625x2 + 0.0625x2

Combine like terms: -0.0625x2 + 0.0625x2 = 0.0000
16 + -2x + 0.0625x2 = 0.0000

Begin completing the square.  Divide all terms by
0.0625 the coefficient of the squared term: 

Divide each side by '0.0625'.
256 + -32x + x2 = 0

Move the constant term to the right:

Add '-256' to each side of the equation.
256 + -32x + -256 + x2 = 0 + -256

Reorder the terms:
256 + -256 + -32x + x2 = 0 + -256

Combine like terms: 256 + -256 = 0
0 + -32x + x2 = 0 + -256
-32x + x2 = 0 + -256

Combine like terms: 0 + -256 = -256
-32x + x2 = -256

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 = -256 + 256

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

Combine like terms: -256 + 256 = 0
256 + -32x + x2 = 0

Factor a perfect square on the left side:
(x + -16)(x + -16) = 0

Calculate the square root of the right side: 0

Break this problem into two subproblems by setting 
(x + -16) equal to 0 and 0.

Subproblem 1

x + -16 = 0 Simplifying x + -16 = 0 Reorder the terms: -16 + x = 0 Solving -16 + x = 0 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 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + x = 0 + 16 x = 0 + 16 Combine like terms: 0 + 16 = 16 x = 16 Simplifying x = 16

Subproblem 2

x + -16 = 0 Simplifying x + -16 = 0 Reorder the terms: -16 + x = 0 Solving -16 + x = 0 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 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + x = 0 + 16 x = 0 + 16 Combine like terms: 0 + 16 = 16 x = 16 Simplifying x = 16

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16, 16}

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