16x-x^2=42

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Solution for 16x-x^2=42 equation:


Simplifying
16x + -1x2 = 42

Solving
16x + -1x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + 16x + -1x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 16x + -1x2 = 0

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

Divide each side by '-1'.
42 + -16x + x2 = 0

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + -16x + -42 + x2 = 0 + -42

Reorder the terms:
42 + -42 + -16x + x2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -16x + x2 = 0 + -42
-16x + x2 = 0 + -42

Combine like terms: 0 + -42 = -42
-16x + x2 = -42

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 = -42 + 64

Reorder the terms:
64 + -16x + x2 = -42 + 64

Combine like terms: -42 + 64 = 22
64 + -16x + x2 = 22

Factor a perfect square on the left side:
(x + -8)(x + -8) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(x + -8) equal to 4.69041576 and -4.69041576.

Subproblem 1

x + -8 = 4.69041576 Simplifying x + -8 = 4.69041576 Reorder the terms: -8 + x = 4.69041576 Solving -8 + x = 4.69041576 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 = 4.69041576 + 8 Combine like terms: -8 + 8 = 0 0 + x = 4.69041576 + 8 x = 4.69041576 + 8 Combine like terms: 4.69041576 + 8 = 12.69041576 x = 12.69041576 Simplifying x = 12.69041576

Subproblem 2

x + -8 = -4.69041576 Simplifying x + -8 = -4.69041576 Reorder the terms: -8 + x = -4.69041576 Solving -8 + x = -4.69041576 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 = -4.69041576 + 8 Combine like terms: -8 + 8 = 0 0 + x = -4.69041576 + 8 x = -4.69041576 + 8 Combine like terms: -4.69041576 + 8 = 3.30958424 x = 3.30958424 Simplifying x = 3.30958424

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.69041576, 3.30958424}

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