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Simplifying 11500 = -143.3x2 + 1823.3x + 6820 Reorder the terms: 11500 = 6820 + 1823.3x + -143.3x2 Solving 11500 = 6820 + 1823.3x + -143.3x2 Solving for variable 'x'. Combine like terms: 11500 + -6820 = 4680 4680 + -1823.3x + 143.3x2 = 6820 + 1823.3x + -143.3x2 + -6820 + -1823.3x + 143.3x2 Reorder the terms: 4680 + -1823.3x + 143.3x2 = 6820 + -6820 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2 Combine like terms: 6820 + -6820 = 0 4680 + -1823.3x + 143.3x2 = 0 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2 4680 + -1823.3x + 143.3x2 = 1823.3x + -1823.3x + -143.3x2 + 143.3x2 Combine like terms: 1823.3x + -1823.3x = 0.0 4680 + -1823.3x + 143.3x2 = 0.0 + -143.3x2 + 143.3x2 4680 + -1823.3x + 143.3x2 = -143.3x2 + 143.3x2 Combine like terms: -143.3x2 + 143.3x2 = 0.0 4680 + -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'. 32.65875785 + -12.72365666x + x2 = 0 Move the constant term to the right: Add '-32.65875785' to each side of the equation. 32.65875785 + -12.72365666x + -32.65875785 + x2 = 0 + -32.65875785 Reorder the terms: 32.65875785 + -32.65875785 + -12.72365666x + x2 = 0 + -32.65875785 Combine like terms: 32.65875785 + -32.65875785 = 0.00000000 0.00000000 + -12.72365666x + x2 = 0 + -32.65875785 -12.72365666x + x2 = 0 + -32.65875785 Combine like terms: 0 + -32.65875785 = -32.65875785 -12.72365666x + x2 = -32.65875785 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 = -32.65875785 + 40.47285970 Reorder the terms: 40.47285970 + -12.72365666x + x2 = -32.65875785 + 40.47285970 Combine like terms: -32.65875785 + 40.47285970 = 7.81410185 40.47285970 + -12.72365666x + x2 = 7.81410185 Factor a perfect square on the left side: (x + -6.36182833)(x + -6.36182833) = 7.81410185 Calculate the square root of the right side: 2.795371505 Break this problem into two subproblems by setting (x + -6.36182833) equal to 2.795371505 and -2.795371505.Subproblem 1
x + -6.36182833 = 2.795371505 Simplifying x + -6.36182833 = 2.795371505 Reorder the terms: -6.36182833 + x = 2.795371505 Solving -6.36182833 + x = 2.795371505 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 = 2.795371505 + 6.36182833 Combine like terms: -6.36182833 + 6.36182833 = 0.00000000 0.00000000 + x = 2.795371505 + 6.36182833 x = 2.795371505 + 6.36182833 Combine like terms: 2.795371505 + 6.36182833 = 9.157199835 x = 9.157199835 Simplifying x = 9.157199835Subproblem 2
x + -6.36182833 = -2.795371505 Simplifying x + -6.36182833 = -2.795371505 Reorder the terms: -6.36182833 + x = -2.795371505 Solving -6.36182833 + x = -2.795371505 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 = -2.795371505 + 6.36182833 Combine like terms: -6.36182833 + 6.36182833 = 0.00000000 0.00000000 + x = -2.795371505 + 6.36182833 x = -2.795371505 + 6.36182833 Combine like terms: -2.795371505 + 6.36182833 = 3.566456825 x = 3.566456825 Simplifying x = 3.566456825Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.157199835, 3.566456825}
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