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Simplifying 0.012x2 + -0.573x + -5.725 = 0 Reorder the terms: -5.725 + -0.573x + 0.012x2 = 0 Solving -5.725 + -0.573x + 0.012x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.012 the coefficient of the squared term: Divide each side by '0.012'. -477.0833333 + -47.75x + x2 = 0 Move the constant term to the right: Add '477.0833333' to each side of the equation. -477.0833333 + -47.75x + 477.0833333 + x2 = 0 + 477.0833333 Reorder the terms: -477.0833333 + 477.0833333 + -47.75x + x2 = 0 + 477.0833333 Combine like terms: -477.0833333 + 477.0833333 = 0.0000000 0.0000000 + -47.75x + x2 = 0 + 477.0833333 -47.75x + x2 = 0 + 477.0833333 Combine like terms: 0 + 477.0833333 = 477.0833333 -47.75x + x2 = 477.0833333 The x term is -47.75x. Take half its coefficient (-23.875). Square it (570.015625) and add it to both sides. Add '570.015625' to each side of the equation. -47.75x + 570.015625 + x2 = 477.0833333 + 570.015625 Reorder the terms: 570.015625 + -47.75x + x2 = 477.0833333 + 570.015625 Combine like terms: 477.0833333 + 570.015625 = 1047.0989583 570.015625 + -47.75x + x2 = 1047.0989583 Factor a perfect square on the left side: (x + -23.875)(x + -23.875) = 1047.0989583 Calculate the square root of the right side: 32.358908484 Break this problem into two subproblems by setting (x + -23.875) equal to 32.358908484 and -32.358908484.Subproblem 1
x + -23.875 = 32.358908484 Simplifying x + -23.875 = 32.358908484 Reorder the terms: -23.875 + x = 32.358908484 Solving -23.875 + x = 32.358908484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.875' to each side of the equation. -23.875 + 23.875 + x = 32.358908484 + 23.875 Combine like terms: -23.875 + 23.875 = 0.000 0.000 + x = 32.358908484 + 23.875 x = 32.358908484 + 23.875 Combine like terms: 32.358908484 + 23.875 = 56.233908484 x = 56.233908484 Simplifying x = 56.233908484Subproblem 2
x + -23.875 = -32.358908484 Simplifying x + -23.875 = -32.358908484 Reorder the terms: -23.875 + x = -32.358908484 Solving -23.875 + x = -32.358908484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.875' to each side of the equation. -23.875 + 23.875 + x = -32.358908484 + 23.875 Combine like terms: -23.875 + 23.875 = 0.000 0.000 + x = -32.358908484 + 23.875 x = -32.358908484 + 23.875 Combine like terms: -32.358908484 + 23.875 = -8.483908484 x = -8.483908484 Simplifying x = -8.483908484Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.233908484, -8.483908484}
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