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Simplifying 12350 = -143.3x2 + 1823.3x + 6820 Reorder the terms: 12350 = 6820 + 1823.3x + -143.3x2 Solving 12350 = 6820 + 1823.3x + -143.3x2 Solving for variable 'x'. Combine like terms: 12350 + -6820 = 5530 5530 + -1823.3x + 143.3x2 = 6820 + 1823.3x + -143.3x2 + -6820 + -1823.3x + 143.3x2 Reorder the terms: 5530 + -1823.3x + 143.3x2 = 6820 + -6820 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2 Combine like terms: 6820 + -6820 = 0 5530 + -1823.3x + 143.3x2 = 0 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2 5530 + -1823.3x + 143.3x2 = 1823.3x + -1823.3x + -143.3x2 + 143.3x2 Combine like terms: 1823.3x + -1823.3x = 0.0 5530 + -1823.3x + 143.3x2 = 0.0 + -143.3x2 + 143.3x2 5530 + -1823.3x + 143.3x2 = -143.3x2 + 143.3x2 Combine like terms: -143.3x2 + 143.3x2 = 0.0 5530 + -1823.3x + 143.3x2 = 0.0 Begin completing the square. Divide all terms by 143.3 the coefficient of the squared term: Divide each side by '143.3'. 38.59036985 + -12.72365666x + x2 = 0 Move the constant term to the right: Add '-38.59036985' to each side of the equation. 38.59036985 + -12.72365666x + -38.59036985 + x2 = 0 + -38.59036985 Reorder the terms: 38.59036985 + -38.59036985 + -12.72365666x + x2 = 0 + -38.59036985 Combine like terms: 38.59036985 + -38.59036985 = 0.00000000 0.00000000 + -12.72365666x + x2 = 0 + -38.59036985 -12.72365666x + x2 = 0 + -38.59036985 Combine like terms: 0 + -38.59036985 = -38.59036985 -12.72365666x + x2 = -38.59036985 The x term is -12.72365666x. Take half its coefficient (-6.36182833). Square it (40.47285970) and add it to both sides. Add '40.47285970' to each side of the equation. -12.72365666x + 40.47285970 + x2 = -38.59036985 + 40.47285970 Reorder the terms: 40.47285970 + -12.72365666x + x2 = -38.59036985 + 40.47285970 Combine like terms: -38.59036985 + 40.47285970 = 1.88248985 40.47285970 + -12.72365666x + x2 = 1.88248985 Factor a perfect square on the left side: (x + -6.36182833)(x + -6.36182833) = 1.88248985 Calculate the square root of the right side: 1.372038575 Break this problem into two subproblems by setting (x + -6.36182833) equal to 1.372038575 and -1.372038575.Subproblem 1
x + -6.36182833 = 1.372038575 Simplifying x + -6.36182833 = 1.372038575 Reorder the terms: -6.36182833 + x = 1.372038575 Solving -6.36182833 + x = 1.372038575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.36182833' to each side of the equation. -6.36182833 + 6.36182833 + x = 1.372038575 + 6.36182833 Combine like terms: -6.36182833 + 6.36182833 = 0.00000000 0.00000000 + x = 1.372038575 + 6.36182833 x = 1.372038575 + 6.36182833 Combine like terms: 1.372038575 + 6.36182833 = 7.733866905 x = 7.733866905 Simplifying x = 7.733866905Subproblem 2
x + -6.36182833 = -1.372038575 Simplifying x + -6.36182833 = -1.372038575 Reorder the terms: -6.36182833 + x = -1.372038575 Solving -6.36182833 + x = -1.372038575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.36182833' to each side of the equation. -6.36182833 + 6.36182833 + x = -1.372038575 + 6.36182833 Combine like terms: -6.36182833 + 6.36182833 = 0.00000000 0.00000000 + x = -1.372038575 + 6.36182833 x = -1.372038575 + 6.36182833 Combine like terms: -1.372038575 + 6.36182833 = 4.989789755 x = 4.989789755 Simplifying x = 4.989789755Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.733866905, 4.989789755}
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