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Simplifying 50x2 + -2.5x + -5025 = 0 Reorder the terms: -5025 + -2.5x + 50x2 = 0 Solving -5025 + -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'. -100.5 + -0.05x + x2 = 0 Move the constant term to the right: Add '100.5' to each side of the equation. -100.5 + -0.05x + 100.5 + x2 = 0 + 100.5 Reorder the terms: -100.5 + 100.5 + -0.05x + x2 = 0 + 100.5 Combine like terms: -100.5 + 100.5 = 0.0 0.0 + -0.05x + x2 = 0 + 100.5 -0.05x + x2 = 0 + 100.5 Combine like terms: 0 + 100.5 = 100.5 -0.05x + x2 = 100.5 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 = 100.5 + 0.000625 Reorder the terms: 0.000625 + -0.05x + x2 = 100.5 + 0.000625 Combine like terms: 100.5 + 0.000625 = 100.500625 0.000625 + -0.05x + x2 = 100.500625 Factor a perfect square on the left side: (x + -0.025)(x + -0.025) = 100.500625 Calculate the square root of the right side: 10.025 Break this problem into two subproblems by setting (x + -0.025) equal to 10.025 and -10.025.Subproblem 1
x + -0.025 = 10.025 Simplifying x + -0.025 = 10.025 Reorder the terms: -0.025 + x = 10.025 Solving -0.025 + x = 10.025 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 = 10.025 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = 10.025 + 0.025 x = 10.025 + 0.025 Combine like terms: 10.025 + 0.025 = 10.05 x = 10.05 Simplifying x = 10.05Subproblem 2
x + -0.025 = -10.025 Simplifying x + -0.025 = -10.025 Reorder the terms: -0.025 + x = -10.025 Solving -0.025 + x = -10.025 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 = -10.025 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = -10.025 + 0.025 x = -10.025 + 0.025 Combine like terms: -10.025 + 0.025 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.05, -10}
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