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Simplifying 50x2 + 3x + -1.5 = 0 Reorder the terms: -1.5 + 3x + 50x2 = 0 Solving -1.5 + 3x + 50x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.03 + 0.06x + x2 = 0 Move the constant term to the right: Add '0.03' to each side of the equation. -0.03 + 0.06x + 0.03 + x2 = 0 + 0.03 Reorder the terms: -0.03 + 0.03 + 0.06x + x2 = 0 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + 0.06x + x2 = 0 + 0.03 0.06x + x2 = 0 + 0.03 Combine like terms: 0 + 0.03 = 0.03 0.06x + x2 = 0.03 The x term is 0.06x. Take half its coefficient (0.03). Square it (0.0009) and add it to both sides. Add '0.0009' to each side of the equation. 0.06x + 0.0009 + x2 = 0.03 + 0.0009 Reorder the terms: 0.0009 + 0.06x + x2 = 0.03 + 0.0009 Combine like terms: 0.03 + 0.0009 = 0.0309 0.0009 + 0.06x + x2 = 0.0309 Factor a perfect square on the left side: (x + 0.03)(x + 0.03) = 0.0309 Calculate the square root of the right side: 0.175783958 Break this problem into two subproblems by setting (x + 0.03) equal to 0.175783958 and -0.175783958.Subproblem 1
x + 0.03 = 0.175783958 Simplifying x + 0.03 = 0.175783958 Reorder the terms: 0.03 + x = 0.175783958 Solving 0.03 + x = 0.175783958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03' to each side of the equation. 0.03 + -0.03 + x = 0.175783958 + -0.03 Combine like terms: 0.03 + -0.03 = 0.00 0.00 + x = 0.175783958 + -0.03 x = 0.175783958 + -0.03 Combine like terms: 0.175783958 + -0.03 = 0.145783958 x = 0.145783958 Simplifying x = 0.145783958Subproblem 2
x + 0.03 = -0.175783958 Simplifying x + 0.03 = -0.175783958 Reorder the terms: 0.03 + x = -0.175783958 Solving 0.03 + x = -0.175783958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03' to each side of the equation. 0.03 + -0.03 + x = -0.175783958 + -0.03 Combine like terms: 0.03 + -0.03 = 0.00 0.00 + x = -0.175783958 + -0.03 x = -0.175783958 + -0.03 Combine like terms: -0.175783958 + -0.03 = -0.205783958 x = -0.205783958 Simplifying x = -0.205783958Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.145783958, -0.205783958}
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