16x-x^2=23.04

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Solution for 16x-x^2=23.04 equation:


Simplifying
16x + -1x2 = 23.04

Solving
16x + -1x2 = 23.04

Solving for variable 'x'.

Reorder the terms:
-23.04 + 16x + -1x2 = 23.04 + -23.04

Combine like terms: 23.04 + -23.04 = 0.00
-23.04 + 16x + -1x2 = 0.00

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

Divide each side by '-1'.
23.04 + -16x + x2 = 0.00

Move the constant term to the right:

Add '-23.04' to each side of the equation.
23.04 + -16x + -23.04 + x2 = 0.00 + -23.04

Reorder the terms:
23.04 + -23.04 + -16x + x2 = 0.00 + -23.04

Combine like terms: 23.04 + -23.04 = 0.00
0.00 + -16x + x2 = 0.00 + -23.04
-16x + x2 = 0.00 + -23.04

Combine like terms: 0.00 + -23.04 = -23.04
-16x + x2 = -23.04

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 = -23.04 + 64

Reorder the terms:
64 + -16x + x2 = -23.04 + 64

Combine like terms: -23.04 + 64 = 40.96
64 + -16x + x2 = 40.96

Factor a perfect square on the left side:
(x + -8)(x + -8) = 40.96

Calculate the square root of the right side: 6.4

Break this problem into two subproblems by setting 
(x + -8) equal to 6.4 and -6.4.

Subproblem 1

x + -8 = 6.4 Simplifying x + -8 = 6.4 Reorder the terms: -8 + x = 6.4 Solving -8 + x = 6.4 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 = 6.4 + 8 Combine like terms: -8 + 8 = 0 0 + x = 6.4 + 8 x = 6.4 + 8 Combine like terms: 6.4 + 8 = 14.4 x = 14.4 Simplifying x = 14.4

Subproblem 2

x + -8 = -6.4 Simplifying x + -8 = -6.4 Reorder the terms: -8 + x = -6.4 Solving -8 + x = -6.4 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 = -6.4 + 8 Combine like terms: -8 + 8 = 0 0 + x = -6.4 + 8 x = -6.4 + 8 Combine like terms: -6.4 + 8 = 1.6 x = 1.6 Simplifying x = 1.6

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.4, 1.6}

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