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Simplifying 6491 = -0.34x2 + 35.51x + 5855.76 Reorder the terms: 6491 = 5855.76 + 35.51x + -0.34x2 Solving 6491 = 5855.76 + 35.51x + -0.34x2 Solving for variable 'x'. Combine like terms: 6491 + -5855.76 = 635.24 635.24 + -35.51x + 0.34x2 = 5855.76 + 35.51x + -0.34x2 + -5855.76 + -35.51x + 0.34x2 Reorder the terms: 635.24 + -35.51x + 0.34x2 = 5855.76 + -5855.76 + 35.51x + -35.51x + -0.34x2 + 0.34x2 Combine like terms: 5855.76 + -5855.76 = 0.00 635.24 + -35.51x + 0.34x2 = 0.00 + 35.51x + -35.51x + -0.34x2 + 0.34x2 635.24 + -35.51x + 0.34x2 = 35.51x + -35.51x + -0.34x2 + 0.34x2 Combine like terms: 35.51x + -35.51x = 0.00 635.24 + -35.51x + 0.34x2 = 0.00 + -0.34x2 + 0.34x2 635.24 + -35.51x + 0.34x2 = -0.34x2 + 0.34x2 Combine like terms: -0.34x2 + 0.34x2 = 0.00 635.24 + -35.51x + 0.34x2 = 0.00 Begin completing the square. Divide all terms by 0.34 the coefficient of the squared term: Divide each side by '0.34'. 1868.352941 + -104.4411765x + x2 = 0 Move the constant term to the right: Add '-1868.352941' to each side of the equation. 1868.352941 + -104.4411765x + -1868.352941 + x2 = 0 + -1868.352941 Reorder the terms: 1868.352941 + -1868.352941 + -104.4411765x + x2 = 0 + -1868.352941 Combine like terms: 1868.352941 + -1868.352941 = 0.000000 0.000000 + -104.4411765x + x2 = 0 + -1868.352941 -104.4411765x + x2 = 0 + -1868.352941 Combine like terms: 0 + -1868.352941 = -1868.352941 -104.4411765x + x2 = -1868.352941 The x term is -104.4411765x. Take half its coefficient (-52.22058825). Square it (2726.989837) and add it to both sides. Add '2726.989837' to each side of the equation. -104.4411765x + 2726.989837 + x2 = -1868.352941 + 2726.989837 Reorder the terms: 2726.989837 + -104.4411765x + x2 = -1868.352941 + 2726.989837 Combine like terms: -1868.352941 + 2726.989837 = 858.636896 2726.989837 + -104.4411765x + x2 = 858.636896 Factor a perfect square on the left side: (x + -52.22058825)(x + -52.22058825) = 858.636896 Calculate the square root of the right side: 29.30250665 Break this problem into two subproblems by setting (x + -52.22058825) equal to 29.30250665 and -29.30250665.Subproblem 1
x + -52.22058825 = 29.30250665 Simplifying x + -52.22058825 = 29.30250665 Reorder the terms: -52.22058825 + x = 29.30250665 Solving -52.22058825 + x = 29.30250665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.22058825' to each side of the equation. -52.22058825 + 52.22058825 + x = 29.30250665 + 52.22058825 Combine like terms: -52.22058825 + 52.22058825 = 0.00000000 0.00000000 + x = 29.30250665 + 52.22058825 x = 29.30250665 + 52.22058825 Combine like terms: 29.30250665 + 52.22058825 = 81.5230949 x = 81.5230949 Simplifying x = 81.5230949Subproblem 2
x + -52.22058825 = -29.30250665 Simplifying x + -52.22058825 = -29.30250665 Reorder the terms: -52.22058825 + x = -29.30250665 Solving -52.22058825 + x = -29.30250665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.22058825' to each side of the equation. -52.22058825 + 52.22058825 + x = -29.30250665 + 52.22058825 Combine like terms: -52.22058825 + 52.22058825 = 0.00000000 0.00000000 + x = -29.30250665 + 52.22058825 x = -29.30250665 + 52.22058825 Combine like terms: -29.30250665 + 52.22058825 = 22.9180816 x = 22.9180816 Simplifying x = 22.9180816Solution
The solution to the problem is based on the solutions from the subproblems. x = {81.5230949, 22.9180816}
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