301x-x^2-8300=0

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Solution for 301x-x^2-8300=0 equation:


Simplifying
301x + -1x2 + -8300 = 0

Reorder the terms:
-8300 + 301x + -1x2 = 0

Solving
-8300 + 301x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
8300 + -301x + x2 = 0

Move the constant term to the right:

Add '-8300' to each side of the equation.
8300 + -301x + -8300 + x2 = 0 + -8300

Reorder the terms:
8300 + -8300 + -301x + x2 = 0 + -8300

Combine like terms: 8300 + -8300 = 0
0 + -301x + x2 = 0 + -8300
-301x + x2 = 0 + -8300

Combine like terms: 0 + -8300 = -8300
-301x + x2 = -8300

The x term is -301x.  Take half its coefficient (-150.5).
Square it (22650.25) and add it to both sides.

Add '22650.25' to each side of the equation.
-301x + 22650.25 + x2 = -8300 + 22650.25

Reorder the terms:
22650.25 + -301x + x2 = -8300 + 22650.25

Combine like terms: -8300 + 22650.25 = 14350.25
22650.25 + -301x + x2 = 14350.25

Factor a perfect square on the left side:
(x + -150.5)(x + -150.5) = 14350.25

Calculate the square root of the right side: 119.792528982

Break this problem into two subproblems by setting 
(x + -150.5) equal to 119.792528982 and -119.792528982.

Subproblem 1

x + -150.5 = 119.792528982 Simplifying x + -150.5 = 119.792528982 Reorder the terms: -150.5 + x = 119.792528982 Solving -150.5 + x = 119.792528982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150.5' to each side of the equation. -150.5 + 150.5 + x = 119.792528982 + 150.5 Combine like terms: -150.5 + 150.5 = 0.0 0.0 + x = 119.792528982 + 150.5 x = 119.792528982 + 150.5 Combine like terms: 119.792528982 + 150.5 = 270.292528982 x = 270.292528982 Simplifying x = 270.292528982

Subproblem 2

x + -150.5 = -119.792528982 Simplifying x + -150.5 = -119.792528982 Reorder the terms: -150.5 + x = -119.792528982 Solving -150.5 + x = -119.792528982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150.5' to each side of the equation. -150.5 + 150.5 + x = -119.792528982 + 150.5 Combine like terms: -150.5 + 150.5 = 0.0 0.0 + x = -119.792528982 + 150.5 x = -119.792528982 + 150.5 Combine like terms: -119.792528982 + 150.5 = 30.707471018 x = 30.707471018 Simplifying x = 30.707471018

Solution

The solution to the problem is based on the solutions from the subproblems. x = {270.292528982, 30.707471018}

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