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Simplifying 0.04x2 + 1.5x + -300 = 0 Reorder the terms: -300 + 1.5x + 0.04x2 = 0 Solving -300 + 1.5x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. -7500 + 37.5x + x2 = 0 Move the constant term to the right: Add '7500' to each side of the equation. -7500 + 37.5x + 7500 + x2 = 0 + 7500 Reorder the terms: -7500 + 7500 + 37.5x + x2 = 0 + 7500 Combine like terms: -7500 + 7500 = 0 0 + 37.5x + x2 = 0 + 7500 37.5x + x2 = 0 + 7500 Combine like terms: 0 + 7500 = 7500 37.5x + x2 = 7500 The x term is 37.5x. Take half its coefficient (18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. 37.5x + 351.5625 + x2 = 7500 + 351.5625 Reorder the terms: 351.5625 + 37.5x + x2 = 7500 + 351.5625 Combine like terms: 7500 + 351.5625 = 7851.5625 351.5625 + 37.5x + x2 = 7851.5625 Factor a perfect square on the left side: (x + 18.75)(x + 18.75) = 7851.5625 Calculate the square root of the right side: 88.609042992 Break this problem into two subproblems by setting (x + 18.75) equal to 88.609042992 and -88.609042992.Subproblem 1
x + 18.75 = 88.609042992 Simplifying x + 18.75 = 88.609042992 Reorder the terms: 18.75 + x = 88.609042992 Solving 18.75 + x = 88.609042992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = 88.609042992 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = 88.609042992 + -18.75 x = 88.609042992 + -18.75 Combine like terms: 88.609042992 + -18.75 = 69.859042992 x = 69.859042992 Simplifying x = 69.859042992Subproblem 2
x + 18.75 = -88.609042992 Simplifying x + 18.75 = -88.609042992 Reorder the terms: 18.75 + x = -88.609042992 Solving 18.75 + x = -88.609042992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = -88.609042992 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = -88.609042992 + -18.75 x = -88.609042992 + -18.75 Combine like terms: -88.609042992 + -18.75 = -107.359042992 x = -107.359042992 Simplifying x = -107.359042992Solution
The solution to the problem is based on the solutions from the subproblems. x = {69.859042992, -107.359042992}
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