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Simplifying 0.01x2 + -5x + -5000 = 0 Reorder the terms: -5000 + -5x + 0.01x2 = 0 Solving -5000 + -5x + 0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. -500000 + -500x + x2 = 0 Move the constant term to the right: Add '500000' to each side of the equation. -500000 + -500x + 500000 + x2 = 0 + 500000 Reorder the terms: -500000 + 500000 + -500x + x2 = 0 + 500000 Combine like terms: -500000 + 500000 = 0 0 + -500x + x2 = 0 + 500000 -500x + x2 = 0 + 500000 Combine like terms: 0 + 500000 = 500000 -500x + x2 = 500000 The x term is -500x. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500x + 62500 + x2 = 500000 + 62500 Reorder the terms: 62500 + -500x + x2 = 500000 + 62500 Combine like terms: 500000 + 62500 = 562500 62500 + -500x + x2 = 562500 Factor a perfect square on the left side: (x + -250)(x + -250) = 562500 Calculate the square root of the right side: 750 Break this problem into two subproblems by setting (x + -250) equal to 750 and -750.Subproblem 1
x + -250 = 750 Simplifying x + -250 = 750 Reorder the terms: -250 + x = 750 Solving -250 + x = 750 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = 750 + 250 Combine like terms: -250 + 250 = 0 0 + x = 750 + 250 x = 750 + 250 Combine like terms: 750 + 250 = 1000 x = 1000 Simplifying x = 1000Subproblem 2
x + -250 = -750 Simplifying x + -250 = -750 Reorder the terms: -250 + x = -750 Solving -250 + x = -750 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = -750 + 250 Combine like terms: -250 + 250 = 0 0 + x = -750 + 250 x = -750 + 250 Combine like terms: -750 + 250 = -500 x = -500 Simplifying x = -500Solution
The solution to the problem is based on the solutions from the subproblems. x = {1000, -500}
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