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Simplifying 0.1025x2 + -0.3076x + 0.9977 = 0.8296 Reorder the terms: 0.9977 + -0.3076x + 0.1025x2 = 0.8296 Solving 0.9977 + -0.3076x + 0.1025x2 = 0.8296 Solving for variable 'x'. Reorder the terms: 0.9977 + -0.8296 + -0.3076x + 0.1025x2 = 0.8296 + -0.8296 Combine like terms: 0.9977 + -0.8296 = 0.1681 0.1681 + -0.3076x + 0.1025x2 = 0.8296 + -0.8296 Combine like terms: 0.8296 + -0.8296 = 0.0000 0.1681 + -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'. 1.64 + -3.00097561x + x2 = 0 Move the constant term to the right: Add '-1.64' to each side of the equation. 1.64 + -3.00097561x + -1.64 + x2 = 0 + -1.64 Reorder the terms: 1.64 + -1.64 + -3.00097561x + x2 = 0 + -1.64 Combine like terms: 1.64 + -1.64 = 0.00 0.00 + -3.00097561x + x2 = 0 + -1.64 -3.00097561x + x2 = 0 + -1.64 Combine like terms: 0 + -1.64 = -1.64 -3.00097561x + x2 = -1.64 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 = -1.64 + 2.251463653 Reorder the terms: 2.251463653 + -3.00097561x + x2 = -1.64 + 2.251463653 Combine like terms: -1.64 + 2.251463653 = 0.611463653 2.251463653 + -3.00097561x + x2 = 0.611463653 Factor a perfect square on the left side: (x + -1.500487805)(x + -1.500487805) = 0.611463653 Calculate the square root of the right side: 0.781961414 Break this problem into two subproblems by setting (x + -1.500487805) equal to 0.781961414 and -0.781961414.Subproblem 1
x + -1.500487805 = 0.781961414 Simplifying x + -1.500487805 = 0.781961414 Reorder the terms: -1.500487805 + x = 0.781961414 Solving -1.500487805 + x = 0.781961414 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 = 0.781961414 + 1.500487805 Combine like terms: -1.500487805 + 1.500487805 = 0.000000000 0.000000000 + x = 0.781961414 + 1.500487805 x = 0.781961414 + 1.500487805 Combine like terms: 0.781961414 + 1.500487805 = 2.282449219 x = 2.282449219 Simplifying x = 2.282449219Subproblem 2
x + -1.500487805 = -0.781961414 Simplifying x + -1.500487805 = -0.781961414 Reorder the terms: -1.500487805 + x = -0.781961414 Solving -1.500487805 + x = -0.781961414 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 = -0.781961414 + 1.500487805 Combine like terms: -1.500487805 + 1.500487805 = 0.000000000 0.000000000 + x = -0.781961414 + 1.500487805 x = -0.781961414 + 1.500487805 Combine like terms: -0.781961414 + 1.500487805 = 0.718526391 x = 0.718526391 Simplifying x = 0.718526391Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.282449219, 0.718526391}
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