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Simplifying 50x2 + 2.5x + -4975 = 0 Reorder the terms: -4975 + 2.5x + 50x2 = 0 Solving -4975 + 2.5x + 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'. -99.5 + 0.05x + x2 = 0 Move the constant term to the right: Add '99.5' to each side of the equation. -99.5 + 0.05x + 99.5 + x2 = 0 + 99.5 Reorder the terms: -99.5 + 99.5 + 0.05x + x2 = 0 + 99.5 Combine like terms: -99.5 + 99.5 = 0.0 0.0 + 0.05x + x2 = 0 + 99.5 0.05x + x2 = 0 + 99.5 Combine like terms: 0 + 99.5 = 99.5 0.05x + x2 = 99.5 The x term is 0.05x. Take half its coefficient (0.025). Square it (0.000625) and add it to both sides. Add '0.000625' to each side of the equation. 0.05x + 0.000625 + x2 = 99.5 + 0.000625 Reorder the terms: 0.000625 + 0.05x + x2 = 99.5 + 0.000625 Combine like terms: 99.5 + 0.000625 = 99.500625 0.000625 + 0.05x + x2 = 99.500625 Factor a perfect square on the left side: (x + 0.025)(x + 0.025) = 99.500625 Calculate the square root of the right side: 9.975 Break this problem into two subproblems by setting (x + 0.025) equal to 9.975 and -9.975.Subproblem 1
x + 0.025 = 9.975 Simplifying x + 0.025 = 9.975 Reorder the terms: 0.025 + x = 9.975 Solving 0.025 + x = 9.975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.025' to each side of the equation. 0.025 + -0.025 + x = 9.975 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + x = 9.975 + -0.025 x = 9.975 + -0.025 Combine like terms: 9.975 + -0.025 = 9.95 x = 9.95 Simplifying x = 9.95Subproblem 2
x + 0.025 = -9.975 Simplifying x + 0.025 = -9.975 Reorder the terms: 0.025 + x = -9.975 Solving 0.025 + x = -9.975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.025' to each side of the equation. 0.025 + -0.025 + x = -9.975 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + x = -9.975 + -0.025 x = -9.975 + -0.025 Combine like terms: -9.975 + -0.025 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.95, -10}
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