x=-x^2+16x+8

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Solution for x=-x^2+16x+8 equation:


Simplifying
x = -1x2 + 16x + 8

Reorder the terms:
x = 8 + 16x + -1x2

Solving
x = 8 + 16x + -1x2

Solving for variable 'x'.

Reorder the terms:
-8 + x + -16x + x2 = 8 + 16x + -1x2 + -8 + -16x + x2

Combine like terms: x + -16x = -15x
-8 + -15x + x2 = 8 + 16x + -1x2 + -8 + -16x + x2

Reorder the terms:
-8 + -15x + x2 = 8 + -8 + 16x + -16x + -1x2 + x2

Combine like terms: 8 + -8 = 0
-8 + -15x + x2 = 0 + 16x + -16x + -1x2 + x2
-8 + -15x + x2 = 16x + -16x + -1x2 + x2

Combine like terms: 16x + -16x = 0
-8 + -15x + x2 = 0 + -1x2 + x2
-8 + -15x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-8 + -15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -15x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -15x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -15x + x2 = 0 + 8
-15x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-15x + x2 = 8

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = 8 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 8 + 56.25

Combine like terms: 8 + 56.25 = 64.25
56.25 + -15x + x2 = 64.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 64.25

Calculate the square root of the right side: 8.015609771

Break this problem into two subproblems by setting 
(x + -7.5) equal to 8.015609771 and -8.015609771.

Subproblem 1

x + -7.5 = 8.015609771 Simplifying x + -7.5 = 8.015609771 Reorder the terms: -7.5 + x = 8.015609771 Solving -7.5 + x = 8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 8.015609771 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.015609771 + 7.5 x = 8.015609771 + 7.5 Combine like terms: 8.015609771 + 7.5 = 15.515609771 x = 15.515609771 Simplifying x = 15.515609771

Subproblem 2

x + -7.5 = -8.015609771 Simplifying x + -7.5 = -8.015609771 Reorder the terms: -7.5 + x = -8.015609771 Solving -7.5 + x = -8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -8.015609771 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.015609771 + 7.5 x = -8.015609771 + 7.5 Combine like terms: -8.015609771 + 7.5 = -0.515609771 x = -0.515609771 Simplifying x = -0.515609771

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.515609771, -0.515609771}

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