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