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Simplifying 0.1025x2 + -0.3076x + 0.9977 = 0.9814 Reorder the terms: 0.9977 + -0.3076x + 0.1025x2 = 0.9814 Solving 0.9977 + -0.3076x + 0.1025x2 = 0.9814 Solving for variable 'x'. Reorder the terms: 0.9977 + -0.9814 + -0.3076x + 0.1025x2 = 0.9814 + -0.9814 Combine like terms: 0.9977 + -0.9814 = 0.0163 0.0163 + -0.3076x + 0.1025x2 = 0.9814 + -0.9814 Combine like terms: 0.9814 + -0.9814 = 0.0000 0.0163 + -0.3076x + 0.1025x2 = 0.0000 Begin completing the square. Divide all terms by 0.1025 the coefficient of the squared term: Divide each side by '0.1025'. 0.1590243902 + -3.00097561x + x2 = 0 Move the constant term to the right: Add '-0.1590243902' to each side of the equation. 0.1590243902 + -3.00097561x + -0.1590243902 + x2 = 0 + -0.1590243902 Reorder the terms: 0.1590243902 + -0.1590243902 + -3.00097561x + x2 = 0 + -0.1590243902 Combine like terms: 0.1590243902 + -0.1590243902 = 0.0000000000 0.0000000000 + -3.00097561x + x2 = 0 + -0.1590243902 -3.00097561x + x2 = 0 + -0.1590243902 Combine like terms: 0 + -0.1590243902 = -0.1590243902 -3.00097561x + x2 = -0.1590243902 The x term is -3.00097561x. Take half its coefficient (-1.500487805). Square it (2.251463653) and add it to both sides. Add '2.251463653' to each side of the equation. -3.00097561x + 2.251463653 + x2 = -0.1590243902 + 2.251463653 Reorder the terms: 2.251463653 + -3.00097561x + x2 = -0.1590243902 + 2.251463653 Combine like terms: -0.1590243902 + 2.251463653 = 2.0924392628 2.251463653 + -3.00097561x + x2 = 2.0924392628 Factor a perfect square on the left side: (x + -1.500487805)(x + -1.500487805) = 2.0924392628 Calculate the square root of the right side: 1.44652662 Break this problem into two subproblems by setting (x + -1.500487805) equal to 1.44652662 and -1.44652662.Subproblem 1
x + -1.500487805 = 1.44652662 Simplifying x + -1.500487805 = 1.44652662 Reorder the terms: -1.500487805 + x = 1.44652662 Solving -1.500487805 + x = 1.44652662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.500487805' to each side of the equation. -1.500487805 + 1.500487805 + x = 1.44652662 + 1.500487805 Combine like terms: -1.500487805 + 1.500487805 = 0.000000000 0.000000000 + x = 1.44652662 + 1.500487805 x = 1.44652662 + 1.500487805 Combine like terms: 1.44652662 + 1.500487805 = 2.947014425 x = 2.947014425 Simplifying x = 2.947014425Subproblem 2
x + -1.500487805 = -1.44652662 Simplifying x + -1.500487805 = -1.44652662 Reorder the terms: -1.500487805 + x = -1.44652662 Solving -1.500487805 + x = -1.44652662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.500487805' to each side of the equation. -1.500487805 + 1.500487805 + x = -1.44652662 + 1.500487805 Combine like terms: -1.500487805 + 1.500487805 = 0.000000000 0.000000000 + x = -1.44652662 + 1.500487805 x = -1.44652662 + 1.500487805 Combine like terms: -1.44652662 + 1.500487805 = 0.053961185 x = 0.053961185 Simplifying x = 0.053961185Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.947014425, 0.053961185}
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