256=160x-x^2

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Solution for 256=160x-x^2 equation:


Simplifying
256 = 160x + -1x2

Solving
256 = 160x + -1x2

Solving for variable 'x'.

Reorder the terms:
256 + -160x + x2 = 160x + -160x + -1x2 + x2

Combine like terms: 160x + -160x = 0
256 + -160x + x2 = 0 + -1x2 + x2
256 + -160x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
256 + -160x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-256' to each side of the equation.
256 + -160x + -256 + x2 = 0 + -256

Reorder the terms:
256 + -256 + -160x + x2 = 0 + -256

Combine like terms: 256 + -256 = 0
0 + -160x + x2 = 0 + -256
-160x + x2 = 0 + -256

Combine like terms: 0 + -256 = -256
-160x + x2 = -256

The x term is -160x.  Take half its coefficient (-80).
Square it (6400) and add it to both sides.

Add '6400' to each side of the equation.
-160x + 6400 + x2 = -256 + 6400

Reorder the terms:
6400 + -160x + x2 = -256 + 6400

Combine like terms: -256 + 6400 = 6144
6400 + -160x + x2 = 6144

Factor a perfect square on the left side:
(x + -80)(x + -80) = 6144

Calculate the square root of the right side: 78.383671769

Break this problem into two subproblems by setting 
(x + -80) equal to 78.383671769 and -78.383671769.

Subproblem 1

x + -80 = 78.383671769 Simplifying x + -80 = 78.383671769 Reorder the terms: -80 + x = 78.383671769 Solving -80 + x = 78.383671769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = 78.383671769 + 80 Combine like terms: -80 + 80 = 0 0 + x = 78.383671769 + 80 x = 78.383671769 + 80 Combine like terms: 78.383671769 + 80 = 158.383671769 x = 158.383671769 Simplifying x = 158.383671769

Subproblem 2

x + -80 = -78.383671769 Simplifying x + -80 = -78.383671769 Reorder the terms: -80 + x = -78.383671769 Solving -80 + x = -78.383671769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = -78.383671769 + 80 Combine like terms: -80 + 80 = 0 0 + x = -78.383671769 + 80 x = -78.383671769 + 80 Combine like terms: -78.383671769 + 80 = 1.616328231 x = 1.616328231 Simplifying x = 1.616328231

Solution

The solution to the problem is based on the solutions from the subproblems. x = {158.383671769, 1.616328231}

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