160=16x-.2x^2

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Solution for 160=16x-.2x^2 equation:


Simplifying
160 = 16x + -0.2x2

Solving
160 = 16x + -0.2x2

Solving for variable 'x'.

Reorder the terms:
160 + -16x + 0.2x2 = 16x + -16x + -0.2x2 + 0.2x2

Combine like terms: 16x + -16x = 0
160 + -16x + 0.2x2 = 0 + -0.2x2 + 0.2x2
160 + -16x + 0.2x2 = -0.2x2 + 0.2x2

Combine like terms: -0.2x2 + 0.2x2 = 0.0
160 + -16x + 0.2x2 = 0.0

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

Divide each side by '0.2'.
800 + -80x + x2 = 0

Move the constant term to the right:

Add '-800' to each side of the equation.
800 + -80x + -800 + x2 = 0 + -800

Reorder the terms:
800 + -800 + -80x + x2 = 0 + -800

Combine like terms: 800 + -800 = 0
0 + -80x + x2 = 0 + -800
-80x + x2 = 0 + -800

Combine like terms: 0 + -800 = -800
-80x + x2 = -800

The x term is -80x.  Take half its coefficient (-40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
-80x + 1600 + x2 = -800 + 1600

Reorder the terms:
1600 + -80x + x2 = -800 + 1600

Combine like terms: -800 + 1600 = 800
1600 + -80x + x2 = 800

Factor a perfect square on the left side:
(x + -40)(x + -40) = 800

Calculate the square root of the right side: 28.284271247

Break this problem into two subproblems by setting 
(x + -40) equal to 28.284271247 and -28.284271247.

Subproblem 1

x + -40 = 28.284271247 Simplifying x + -40 = 28.284271247 Reorder the terms: -40 + x = 28.284271247 Solving -40 + x = 28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 28.284271247 + 40 Combine like terms: -40 + 40 = 0 0 + x = 28.284271247 + 40 x = 28.284271247 + 40 Combine like terms: 28.284271247 + 40 = 68.284271247 x = 68.284271247 Simplifying x = 68.284271247

Subproblem 2

x + -40 = -28.284271247 Simplifying x + -40 = -28.284271247 Reorder the terms: -40 + x = -28.284271247 Solving -40 + x = -28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -28.284271247 + 40 Combine like terms: -40 + 40 = 0 0 + x = -28.284271247 + 40 x = -28.284271247 + 40 Combine like terms: -28.284271247 + 40 = 11.715728753 x = 11.715728753 Simplifying x = 11.715728753

Solution

The solution to the problem is based on the solutions from the subproblems. x = {68.284271247, 11.715728753}

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