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Simplifying 500x + -2x2 = 300x + 3080 Reorder the terms: 500x + -2x2 = 3080 + 300x Solving 500x + -2x2 = 3080 + 300x Solving for variable 'x'. Reorder the terms: -3080 + 500x + -300x + -2x2 = 3080 + 300x + -3080 + -300x Combine like terms: 500x + -300x = 200x -3080 + 200x + -2x2 = 3080 + 300x + -3080 + -300x Reorder the terms: -3080 + 200x + -2x2 = 3080 + -3080 + 300x + -300x Combine like terms: 3080 + -3080 = 0 -3080 + 200x + -2x2 = 0 + 300x + -300x -3080 + 200x + -2x2 = 300x + -300x Combine like terms: 300x + -300x = 0 -3080 + 200x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1540 + 100x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1540 + 100x + -1x2)' equal to zero and attempt to solve: Simplifying -1540 + 100x + -1x2 = 0 Solving -1540 + 100x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1540 + -100x + x2 = 0 Move the constant term to the right: Add '-1540' to each side of the equation. 1540 + -100x + -1540 + x2 = 0 + -1540 Reorder the terms: 1540 + -1540 + -100x + x2 = 0 + -1540 Combine like terms: 1540 + -1540 = 0 0 + -100x + x2 = 0 + -1540 -100x + x2 = 0 + -1540 Combine like terms: 0 + -1540 = -1540 -100x + x2 = -1540 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -1540 + 2500 Reorder the terms: 2500 + -100x + x2 = -1540 + 2500 Combine like terms: -1540 + 2500 = 960 2500 + -100x + x2 = 960 Factor a perfect square on the left side: (x + -50)(x + -50) = 960 Calculate the square root of the right side: 30.98386677 Break this problem into two subproblems by setting (x + -50) equal to 30.98386677 and -30.98386677.Subproblem 1
x + -50 = 30.98386677 Simplifying x + -50 = 30.98386677 Reorder the terms: -50 + x = 30.98386677 Solving -50 + x = 30.98386677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 30.98386677 + 50 Combine like terms: -50 + 50 = 0 0 + x = 30.98386677 + 50 x = 30.98386677 + 50 Combine like terms: 30.98386677 + 50 = 80.98386677 x = 80.98386677 Simplifying x = 80.98386677Subproblem 2
x + -50 = -30.98386677 Simplifying x + -50 = -30.98386677 Reorder the terms: -50 + x = -30.98386677 Solving -50 + x = -30.98386677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -30.98386677 + 50 Combine like terms: -50 + 50 = 0 0 + x = -30.98386677 + 50 x = -30.98386677 + 50 Combine like terms: -30.98386677 + 50 = 19.01613323 x = 19.01613323 Simplifying x = 19.01613323Solution
The solution to the problem is based on the solutions from the subproblems. x = {80.98386677, 19.01613323}Solution
x = {80.98386677, 19.01613323}
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