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Simplifying -0.08x2 + 80x + -1500 = 0 Reorder the terms: -1500 + 80x + -0.08x2 = 0 Solving -1500 + 80x + -0.08x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.08 the coefficient of the squared term: Divide each side by '-0.08'. 18750 + -1000x + x2 = 0 Move the constant term to the right: Add '-18750' to each side of the equation. 18750 + -1000x + -18750 + x2 = 0 + -18750 Reorder the terms: 18750 + -18750 + -1000x + x2 = 0 + -18750 Combine like terms: 18750 + -18750 = 0 0 + -1000x + x2 = 0 + -18750 -1000x + x2 = 0 + -18750 Combine like terms: 0 + -18750 = -18750 -1000x + x2 = -18750 The x term is -1000x. Take half its coefficient (-500). Square it (250000) and add it to both sides. Add '250000' to each side of the equation. -1000x + 250000 + x2 = -18750 + 250000 Reorder the terms: 250000 + -1000x + x2 = -18750 + 250000 Combine like terms: -18750 + 250000 = 231250 250000 + -1000x + x2 = 231250 Factor a perfect square on the left side: (x + -500)(x + -500) = 231250 Calculate the square root of the right side: 480.884601542 Break this problem into two subproblems by setting (x + -500) equal to 480.884601542 and -480.884601542.Subproblem 1
x + -500 = 480.884601542 Simplifying x + -500 = 480.884601542 Reorder the terms: -500 + x = 480.884601542 Solving -500 + x = 480.884601542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = 480.884601542 + 500 Combine like terms: -500 + 500 = 0 0 + x = 480.884601542 + 500 x = 480.884601542 + 500 Combine like terms: 480.884601542 + 500 = 980.884601542 x = 980.884601542 Simplifying x = 980.884601542Subproblem 2
x + -500 = -480.884601542 Simplifying x + -500 = -480.884601542 Reorder the terms: -500 + x = -480.884601542 Solving -500 + x = -480.884601542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = -480.884601542 + 500 Combine like terms: -500 + 500 = 0 0 + x = -480.884601542 + 500 x = -480.884601542 + 500 Combine like terms: -480.884601542 + 500 = 19.115398458 x = 19.115398458 Simplifying x = 19.115398458Solution
The solution to the problem is based on the solutions from the subproblems. x = {980.884601542, 19.115398458}
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