0=-x^2+160x-100

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Solution for 0=-x^2+160x-100 equation:


Simplifying
0 = -1x2 + 160x + -100

Reorder the terms:
0 = -100 + 160x + -1x2

Solving
0 = -100 + 160x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 100 = 100
100 + -160x + x2 = -100 + 160x + -1x2 + 100 + -160x + x2

Reorder the terms:
100 + -160x + x2 = -100 + 100 + 160x + -160x + -1x2 + x2

Combine like terms: -100 + 100 = 0
100 + -160x + x2 = 0 + 160x + -160x + -1x2 + x2
100 + -160x + x2 = 160x + -160x + -1x2 + x2

Combine like terms: 160x + -160x = 0
100 + -160x + x2 = 0 + -1x2 + x2
100 + -160x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
100 + -160x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -160x + -100 + x2 = 0 + -100

Reorder the terms:
100 + -100 + -160x + x2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -160x + x2 = 0 + -100
-160x + x2 = 0 + -100

Combine like terms: 0 + -100 = -100
-160x + x2 = -100

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 = -100 + 6400

Reorder the terms:
6400 + -160x + x2 = -100 + 6400

Combine like terms: -100 + 6400 = 6300
6400 + -160x + x2 = 6300

Factor a perfect square on the left side:
(x + -80)(x + -80) = 6300

Calculate the square root of the right side: 79.372539332

Break this problem into two subproblems by setting 
(x + -80) equal to 79.372539332 and -79.372539332.

Subproblem 1

x + -80 = 79.372539332 Simplifying x + -80 = 79.372539332 Reorder the terms: -80 + x = 79.372539332 Solving -80 + x = 79.372539332 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 = 79.372539332 + 80 Combine like terms: -80 + 80 = 0 0 + x = 79.372539332 + 80 x = 79.372539332 + 80 Combine like terms: 79.372539332 + 80 = 159.372539332 x = 159.372539332 Simplifying x = 159.372539332

Subproblem 2

x + -80 = -79.372539332 Simplifying x + -80 = -79.372539332 Reorder the terms: -80 + x = -79.372539332 Solving -80 + x = -79.372539332 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 = -79.372539332 + 80 Combine like terms: -80 + 80 = 0 0 + x = -79.372539332 + 80 x = -79.372539332 + 80 Combine like terms: -79.372539332 + 80 = 0.627460668 x = 0.627460668 Simplifying x = 0.627460668

Solution

The solution to the problem is based on the solutions from the subproblems. x = {159.372539332, 0.627460668}

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