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Simplifying -0.05x2 + 30x + -2500 = 0 Reorder the terms: -2500 + 30x + -0.05x2 = 0 Solving -2500 + 30x + -0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. 50000 + -600x + x2 = 0 Move the constant term to the right: Add '-50000' to each side of the equation. 50000 + -600x + -50000 + x2 = 0 + -50000 Reorder the terms: 50000 + -50000 + -600x + x2 = 0 + -50000 Combine like terms: 50000 + -50000 = 0 0 + -600x + x2 = 0 + -50000 -600x + x2 = 0 + -50000 Combine like terms: 0 + -50000 = -50000 -600x + x2 = -50000 The x term is -600x. Take half its coefficient (-300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. -600x + 90000 + x2 = -50000 + 90000 Reorder the terms: 90000 + -600x + x2 = -50000 + 90000 Combine like terms: -50000 + 90000 = 40000 90000 + -600x + x2 = 40000 Factor a perfect square on the left side: (x + -300)(x + -300) = 40000 Calculate the square root of the right side: 200 Break this problem into two subproblems by setting (x + -300) equal to 200 and -200.Subproblem 1
x + -300 = 200 Simplifying x + -300 = 200 Reorder the terms: -300 + x = 200 Solving -300 + x = 200 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = 200 + 300 Combine like terms: -300 + 300 = 0 0 + x = 200 + 300 x = 200 + 300 Combine like terms: 200 + 300 = 500 x = 500 Simplifying x = 500Subproblem 2
x + -300 = -200 Simplifying x + -300 = -200 Reorder the terms: -300 + x = -200 Solving -300 + x = -200 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = -200 + 300 Combine like terms: -300 + 300 = 0 0 + x = -200 + 300 x = -200 + 300 Combine like terms: -200 + 300 = 100 x = 100 Simplifying x = 100Solution
The solution to the problem is based on the solutions from the subproblems. x = {500, 100}
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