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Simplifying 20x2 + -1x + -100 = 0 Reorder the terms: -100 + -1x + 20x2 = 0 Solving -100 + -1x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -5 + -0.05x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.05x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -0.05x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.05x + x2 = 0 + 5 -0.05x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.05x + x2 = 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 = 5 + 0.000625 Reorder the terms: 0.000625 + -0.05x + x2 = 5 + 0.000625 Combine like terms: 5 + 0.000625 = 5.000625 0.000625 + -0.05x + x2 = 5.000625 Factor a perfect square on the left side: (x + -0.025)(x + -0.025) = 5.000625 Calculate the square root of the right side: 2.236207727 Break this problem into two subproblems by setting (x + -0.025) equal to 2.236207727 and -2.236207727.Subproblem 1
x + -0.025 = 2.236207727 Simplifying x + -0.025 = 2.236207727 Reorder the terms: -0.025 + x = 2.236207727 Solving -0.025 + x = 2.236207727 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 = 2.236207727 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = 2.236207727 + 0.025 x = 2.236207727 + 0.025 Combine like terms: 2.236207727 + 0.025 = 2.261207727 x = 2.261207727 Simplifying x = 2.261207727Subproblem 2
x + -0.025 = -2.236207727 Simplifying x + -0.025 = -2.236207727 Reorder the terms: -0.025 + x = -2.236207727 Solving -0.025 + x = -2.236207727 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 = -2.236207727 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = -2.236207727 + 0.025 x = -2.236207727 + 0.025 Combine like terms: -2.236207727 + 0.025 = -2.211207727 x = -2.211207727 Simplifying x = -2.211207727Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.261207727, -2.211207727}
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