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Simplifying -0.062x2 + 1.4647x + 5.2405 = 5 Reorder the terms: 5.2405 + 1.4647x + -0.062x2 = 5 Solving 5.2405 + 1.4647x + -0.062x2 = 5 Solving for variable 'x'. Reorder the terms: 5.2405 + -5 + 1.4647x + -0.062x2 = 5 + -5 Combine like terms: 5.2405 + -5 = 0.2405 0.2405 + 1.4647x + -0.062x2 = 5 + -5 Combine like terms: 5 + -5 = 0 0.2405 + 1.4647x + -0.062x2 = 0 Begin completing the square. Divide all terms by -0.062 the coefficient of the squared term: Divide each side by '-0.062'. -3.879032258 + -23.62419355x + x2 = 0 Move the constant term to the right: Add '3.879032258' to each side of the equation. -3.879032258 + -23.62419355x + 3.879032258 + x2 = 0 + 3.879032258 Reorder the terms: -3.879032258 + 3.879032258 + -23.62419355x + x2 = 0 + 3.879032258 Combine like terms: -3.879032258 + 3.879032258 = 0.000000000 0.000000000 + -23.62419355x + x2 = 0 + 3.879032258 -23.62419355x + x2 = 0 + 3.879032258 Combine like terms: 0 + 3.879032258 = 3.879032258 -23.62419355x + x2 = 3.879032258 The x term is -23.62419355x. Take half its coefficient (-11.81209678). Square it (139.5256303) and add it to both sides. Add '139.5256303' to each side of the equation. -23.62419355x + 139.5256303 + x2 = 3.879032258 + 139.5256303 Reorder the terms: 139.5256303 + -23.62419355x + x2 = 3.879032258 + 139.5256303 Combine like terms: 3.879032258 + 139.5256303 = 143.404662558 139.5256303 + -23.62419355x + x2 = 143.404662558 Factor a perfect square on the left side: (x + -11.81209678)(x + -11.81209678) = 143.404662558 Calculate the square root of the right side: 11.975168582 Break this problem into two subproblems by setting (x + -11.81209678) equal to 11.975168582 and -11.975168582.Subproblem 1
x + -11.81209678 = 11.975168582 Simplifying x + -11.81209678 = 11.975168582 Reorder the terms: -11.81209678 + x = 11.975168582 Solving -11.81209678 + x = 11.975168582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.81209678' to each side of the equation. -11.81209678 + 11.81209678 + x = 11.975168582 + 11.81209678 Combine like terms: -11.81209678 + 11.81209678 = 0.00000000 0.00000000 + x = 11.975168582 + 11.81209678 x = 11.975168582 + 11.81209678 Combine like terms: 11.975168582 + 11.81209678 = 23.787265362 x = 23.787265362 Simplifying x = 23.787265362Subproblem 2
x + -11.81209678 = -11.975168582 Simplifying x + -11.81209678 = -11.975168582 Reorder the terms: -11.81209678 + x = -11.975168582 Solving -11.81209678 + x = -11.975168582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.81209678' to each side of the equation. -11.81209678 + 11.81209678 + x = -11.975168582 + 11.81209678 Combine like terms: -11.81209678 + 11.81209678 = 0.00000000 0.00000000 + x = -11.975168582 + 11.81209678 x = -11.975168582 + 11.81209678 Combine like terms: -11.975168582 + 11.81209678 = -0.163071802 x = -0.163071802 Simplifying x = -0.163071802Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.787265362, -0.163071802}
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