0=-360+150x-x^2

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Solution for 0=-360+150x-x^2 equation:


Simplifying
0 = -360 + 150x + -1x2

Solving
0 = -360 + 150x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 360 = 360
360 + -150x + x2 = -360 + 150x + -1x2 + 360 + -150x + x2

Reorder the terms:
360 + -150x + x2 = -360 + 360 + 150x + -150x + -1x2 + x2

Combine like terms: -360 + 360 = 0
360 + -150x + x2 = 0 + 150x + -150x + -1x2 + x2
360 + -150x + x2 = 150x + -150x + -1x2 + x2

Combine like terms: 150x + -150x = 0
360 + -150x + x2 = 0 + -1x2 + x2
360 + -150x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
360 + -150x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-360' to each side of the equation.
360 + -150x + -360 + x2 = 0 + -360

Reorder the terms:
360 + -360 + -150x + x2 = 0 + -360

Combine like terms: 360 + -360 = 0
0 + -150x + x2 = 0 + -360
-150x + x2 = 0 + -360

Combine like terms: 0 + -360 = -360
-150x + x2 = -360

The x term is -150x.  Take half its coefficient (-75).
Square it (5625) and add it to both sides.

Add '5625' to each side of the equation.
-150x + 5625 + x2 = -360 + 5625

Reorder the terms:
5625 + -150x + x2 = -360 + 5625

Combine like terms: -360 + 5625 = 5265
5625 + -150x + x2 = 5265

Factor a perfect square on the left side:
(x + -75)(x + -75) = 5265

Calculate the square root of the right side: 72.560319735

Break this problem into two subproblems by setting 
(x + -75) equal to 72.560319735 and -72.560319735.

Subproblem 1

x + -75 = 72.560319735 Simplifying x + -75 = 72.560319735 Reorder the terms: -75 + x = 72.560319735 Solving -75 + x = 72.560319735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = 72.560319735 + 75 Combine like terms: -75 + 75 = 0 0 + x = 72.560319735 + 75 x = 72.560319735 + 75 Combine like terms: 72.560319735 + 75 = 147.560319735 x = 147.560319735 Simplifying x = 147.560319735

Subproblem 2

x + -75 = -72.560319735 Simplifying x + -75 = -72.560319735 Reorder the terms: -75 + x = -72.560319735 Solving -75 + x = -72.560319735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = -72.560319735 + 75 Combine like terms: -75 + 75 = 0 0 + x = -72.560319735 + 75 x = -72.560319735 + 75 Combine like terms: -72.560319735 + 75 = 2.439680265 x = 2.439680265 Simplifying x = 2.439680265

Solution

The solution to the problem is based on the solutions from the subproblems. x = {147.560319735, 2.439680265}

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