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Simplifying 1995 = -143.3x2 + 1823.3x + 6820 Reorder the terms: 1995 = 6820 + 1823.3x + -143.3x2 Solving 1995 = 6820 + 1823.3x + -143.3x2 Solving for variable 'x'. Combine like terms: 1995 + -6820 = -4825 -4825 + -1823.3x + 143.3x2 = 6820 + 1823.3x + -143.3x2 + -6820 + -1823.3x + 143.3x2 Reorder the terms: -4825 + -1823.3x + 143.3x2 = 6820 + -6820 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2 Combine like terms: 6820 + -6820 = 0 -4825 + -1823.3x + 143.3x2 = 0 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2 -4825 + -1823.3x + 143.3x2 = 1823.3x + -1823.3x + -143.3x2 + 143.3x2 Combine like terms: 1823.3x + -1823.3x = 0.0 -4825 + -1823.3x + 143.3x2 = 0.0 + -143.3x2 + 143.3x2 -4825 + -1823.3x + 143.3x2 = -143.3x2 + 143.3x2 Combine like terms: -143.3x2 + 143.3x2 = 0.0 -4825 + -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'. -33.67062107 + -12.72365666x + x2 = 0 Move the constant term to the right: Add '33.67062107' to each side of the equation. -33.67062107 + -12.72365666x + 33.67062107 + x2 = 0 + 33.67062107 Reorder the terms: -33.67062107 + 33.67062107 + -12.72365666x + x2 = 0 + 33.67062107 Combine like terms: -33.67062107 + 33.67062107 = 0.00000000 0.00000000 + -12.72365666x + x2 = 0 + 33.67062107 -12.72365666x + x2 = 0 + 33.67062107 Combine like terms: 0 + 33.67062107 = 33.67062107 -12.72365666x + x2 = 33.67062107 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 = 33.67062107 + 40.47285970 Reorder the terms: 40.47285970 + -12.72365666x + x2 = 33.67062107 + 40.47285970 Combine like terms: 33.67062107 + 40.47285970 = 74.14348077 40.47285970 + -12.72365666x + x2 = 74.14348077 Factor a perfect square on the left side: (x + -6.36182833)(x + -6.36182833) = 74.14348077 Calculate the square root of the right side: 8.610660879 Break this problem into two subproblems by setting (x + -6.36182833) equal to 8.610660879 and -8.610660879.Subproblem 1
x + -6.36182833 = 8.610660879 Simplifying x + -6.36182833 = 8.610660879 Reorder the terms: -6.36182833 + x = 8.610660879 Solving -6.36182833 + x = 8.610660879 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 = 8.610660879 + 6.36182833 Combine like terms: -6.36182833 + 6.36182833 = 0.00000000 0.00000000 + x = 8.610660879 + 6.36182833 x = 8.610660879 + 6.36182833 Combine like terms: 8.610660879 + 6.36182833 = 14.972489209 x = 14.972489209 Simplifying x = 14.972489209Subproblem 2
x + -6.36182833 = -8.610660879 Simplifying x + -6.36182833 = -8.610660879 Reorder the terms: -6.36182833 + x = -8.610660879 Solving -6.36182833 + x = -8.610660879 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 = -8.610660879 + 6.36182833 Combine like terms: -6.36182833 + 6.36182833 = 0.00000000 0.00000000 + x = -8.610660879 + 6.36182833 x = -8.610660879 + 6.36182833 Combine like terms: -8.610660879 + 6.36182833 = -2.248832549 x = -2.248832549 Simplifying x = -2.248832549Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.972489209, -2.248832549}
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