16x-x^2=24

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Solution for 16x-x^2=24 equation:


Simplifying
16x + -1x2 = 24

Solving
16x + -1x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 16x + -1x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 16x + -1x2 = 0

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

Divide each side by '-1'.
24 + -16x + x2 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -16x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -16x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -16x + x2 = 0 + -24
-16x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-16x + x2 = -24

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 = -24 + 64

Reorder the terms:
64 + -16x + x2 = -24 + 64

Combine like terms: -24 + 64 = 40
64 + -16x + x2 = 40

Factor a perfect square on the left side:
(x + -8)(x + -8) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + -8) equal to 6.32455532 and -6.32455532.

Subproblem 1

x + -8 = 6.32455532 Simplifying x + -8 = 6.32455532 Reorder the terms: -8 + x = 6.32455532 Solving -8 + x = 6.32455532 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 = 6.32455532 + 8 Combine like terms: -8 + 8 = 0 0 + x = 6.32455532 + 8 x = 6.32455532 + 8 Combine like terms: 6.32455532 + 8 = 14.32455532 x = 14.32455532 Simplifying x = 14.32455532

Subproblem 2

x + -8 = -6.32455532 Simplifying x + -8 = -6.32455532 Reorder the terms: -8 + x = -6.32455532 Solving -8 + x = -6.32455532 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 = -6.32455532 + 8 Combine like terms: -8 + 8 = 0 0 + x = -6.32455532 + 8 x = -6.32455532 + 8 Combine like terms: -6.32455532 + 8 = 1.67544468 x = 1.67544468 Simplifying x = 1.67544468

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.32455532, 1.67544468}

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