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Simplifying 0 = -0.005x2 + 0.17x + 3 Reorder the terms: 0 = 3 + 0.17x + -0.005x2 Solving 0 = 3 + 0.17x + -0.005x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -0.17x + 0.005x2 = 3 + 0.17x + -0.005x2 + -3 + -0.17x + 0.005x2 Reorder the terms: -3 + -0.17x + 0.005x2 = 3 + -3 + 0.17x + -0.17x + -0.005x2 + 0.005x2 Combine like terms: 3 + -3 = 0 -3 + -0.17x + 0.005x2 = 0 + 0.17x + -0.17x + -0.005x2 + 0.005x2 -3 + -0.17x + 0.005x2 = 0.17x + -0.17x + -0.005x2 + 0.005x2 Combine like terms: 0.17x + -0.17x = 0.00 -3 + -0.17x + 0.005x2 = 0.00 + -0.005x2 + 0.005x2 -3 + -0.17x + 0.005x2 = -0.005x2 + 0.005x2 Combine like terms: -0.005x2 + 0.005x2 = 0.000 -3 + -0.17x + 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'. -600 + -34x + x2 = 0 Move the constant term to the right: Add '600' to each side of the equation. -600 + -34x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + -34x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + -34x + x2 = 0 + 600 -34x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 -34x + x2 = 600 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = 600 + 289 Reorder the terms: 289 + -34x + x2 = 600 + 289 Combine like terms: 600 + 289 = 889 289 + -34x + x2 = 889 Factor a perfect square on the left side: (x + -17)(x + -17) = 889 Calculate the square root of the right side: 29.816103032 Break this problem into two subproblems by setting (x + -17) equal to 29.816103032 and -29.816103032.Subproblem 1
x + -17 = 29.816103032 Simplifying x + -17 = 29.816103032 Reorder the terms: -17 + x = 29.816103032 Solving -17 + x = 29.816103032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 29.816103032 + 17 Combine like terms: -17 + 17 = 0 0 + x = 29.816103032 + 17 x = 29.816103032 + 17 Combine like terms: 29.816103032 + 17 = 46.816103032 x = 46.816103032 Simplifying x = 46.816103032Subproblem 2
x + -17 = -29.816103032 Simplifying x + -17 = -29.816103032 Reorder the terms: -17 + x = -29.816103032 Solving -17 + x = -29.816103032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -29.816103032 + 17 Combine like terms: -17 + 17 = 0 0 + x = -29.816103032 + 17 x = -29.816103032 + 17 Combine like terms: -29.816103032 + 17 = -12.816103032 x = -12.816103032 Simplifying x = -12.816103032Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.816103032, -12.816103032}
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