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Simplifying 3 = -0.05x2 + 2x + 1.5 Reorder the terms: 3 = 1.5 + 2x + -0.05x2 Solving 3 = 1.5 + 2x + -0.05x2 Solving for variable 'x'. Combine like terms: 3 + -1.5 = 1.5 1.5 + -2x + 0.05x2 = 1.5 + 2x + -0.05x2 + -1.5 + -2x + 0.05x2 Reorder the terms: 1.5 + -2x + 0.05x2 = 1.5 + -1.5 + 2x + -2x + -0.05x2 + 0.05x2 Combine like terms: 1.5 + -1.5 = 0.0 1.5 + -2x + 0.05x2 = 0.0 + 2x + -2x + -0.05x2 + 0.05x2 1.5 + -2x + 0.05x2 = 2x + -2x + -0.05x2 + 0.05x2 Combine like terms: 2x + -2x = 0 1.5 + -2x + 0.05x2 = 0 + -0.05x2 + 0.05x2 1.5 + -2x + 0.05x2 = -0.05x2 + 0.05x2 Combine like terms: -0.05x2 + 0.05x2 = 0.00 1.5 + -2x + 0.05x2 = 0.00 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. 30 + -40x + x2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -40x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -40x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -40x + x2 = 0 + -30 -40x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -40x + x2 = -30 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -30 + 400 Reorder the terms: 400 + -40x + x2 = -30 + 400 Combine like terms: -30 + 400 = 370 400 + -40x + x2 = 370 Factor a perfect square on the left side: (x + -20)(x + -20) = 370 Calculate the square root of the right side: 19.235384062 Break this problem into two subproblems by setting (x + -20) equal to 19.235384062 and -19.235384062.Subproblem 1
x + -20 = 19.235384062 Simplifying x + -20 = 19.235384062 Reorder the terms: -20 + x = 19.235384062 Solving -20 + x = 19.235384062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 19.235384062 + 20 Combine like terms: -20 + 20 = 0 0 + x = 19.235384062 + 20 x = 19.235384062 + 20 Combine like terms: 19.235384062 + 20 = 39.235384062 x = 39.235384062 Simplifying x = 39.235384062Subproblem 2
x + -20 = -19.235384062 Simplifying x + -20 = -19.235384062 Reorder the terms: -20 + x = -19.235384062 Solving -20 + x = -19.235384062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -19.235384062 + 20 Combine like terms: -20 + 20 = 0 0 + x = -19.235384062 + 20 x = -19.235384062 + 20 Combine like terms: -19.235384062 + 20 = 0.764615938 x = 0.764615938 Simplifying x = 0.764615938Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.235384062, 0.764615938}
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