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Simplifying 0 = -0.005x2 + 0.41x + -5.1 Reorder the terms: 0 = -5.1 + 0.41x + -0.005x2 Solving 0 = -5.1 + 0.41x + -0.005x2 Solving for variable 'x'. Combine like terms: 0 + 5.1 = 5.1 5.1 + -0.41x + 0.005x2 = -5.1 + 0.41x + -0.005x2 + 5.1 + -0.41x + 0.005x2 Reorder the terms: 5.1 + -0.41x + 0.005x2 = -5.1 + 5.1 + 0.41x + -0.41x + -0.005x2 + 0.005x2 Combine like terms: -5.1 + 5.1 = 0.0 5.1 + -0.41x + 0.005x2 = 0.0 + 0.41x + -0.41x + -0.005x2 + 0.005x2 5.1 + -0.41x + 0.005x2 = 0.41x + -0.41x + -0.005x2 + 0.005x2 Combine like terms: 0.41x + -0.41x = 0.00 5.1 + -0.41x + 0.005x2 = 0.00 + -0.005x2 + 0.005x2 5.1 + -0.41x + 0.005x2 = -0.005x2 + 0.005x2 Combine like terms: -0.005x2 + 0.005x2 = 0.000 5.1 + -0.41x + 0.005x2 = 0.000 Begin completing the square. Divide all terms by 0.005 the coefficient of the squared term: Divide each side by '0.005'. 1020 + -82x + x2 = 0 Move the constant term to the right: Add '-1020' to each side of the equation. 1020 + -82x + -1020 + x2 = 0 + -1020 Reorder the terms: 1020 + -1020 + -82x + x2 = 0 + -1020 Combine like terms: 1020 + -1020 = 0 0 + -82x + x2 = 0 + -1020 -82x + x2 = 0 + -1020 Combine like terms: 0 + -1020 = -1020 -82x + x2 = -1020 The x term is -82x. Take half its coefficient (-41). Square it (1681) and add it to both sides. Add '1681' to each side of the equation. -82x + 1681 + x2 = -1020 + 1681 Reorder the terms: 1681 + -82x + x2 = -1020 + 1681 Combine like terms: -1020 + 1681 = 661 1681 + -82x + x2 = 661 Factor a perfect square on the left side: (x + -41)(x + -41) = 661 Calculate the square root of the right side: 25.709920264 Break this problem into two subproblems by setting (x + -41) equal to 25.709920264 and -25.709920264.Subproblem 1
x + -41 = 25.709920264 Simplifying x + -41 = 25.709920264 Reorder the terms: -41 + x = 25.709920264 Solving -41 + x = 25.709920264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41' to each side of the equation. -41 + 41 + x = 25.709920264 + 41 Combine like terms: -41 + 41 = 0 0 + x = 25.709920264 + 41 x = 25.709920264 + 41 Combine like terms: 25.709920264 + 41 = 66.709920264 x = 66.709920264 Simplifying x = 66.709920264Subproblem 2
x + -41 = -25.709920264 Simplifying x + -41 = -25.709920264 Reorder the terms: -41 + x = -25.709920264 Solving -41 + x = -25.709920264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41' to each side of the equation. -41 + 41 + x = -25.709920264 + 41 Combine like terms: -41 + 41 = 0 0 + x = -25.709920264 + 41 x = -25.709920264 + 41 Combine like terms: -25.709920264 + 41 = 15.290079736 x = 15.290079736 Simplifying x = 15.290079736Solution
The solution to the problem is based on the solutions from the subproblems. x = {66.709920264, 15.290079736}
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