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Simplifying 11000 = -143.3x2 + 1823.3x + 6820 Reorder the terms: 11000 = 6820 + 1823.3x + -143.3x2 Solving 11000 = 6820 + 1823.3x + -143.3x2 Solving for variable 'x'. Combine like terms: 11000 + -6820 = 4180 4180 + -1823.3x + 143.3x2 = 6820 + 1823.3x + -143.3x2 + -6820 + -1823.3x + 143.3x2 Reorder the terms: 4180 + -1823.3x + 143.3x2 = 6820 + -6820 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2 Combine like terms: 6820 + -6820 = 0 4180 + -1823.3x + 143.3x2 = 0 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2 4180 + -1823.3x + 143.3x2 = 1823.3x + -1823.3x + -143.3x2 + 143.3x2 Combine like terms: 1823.3x + -1823.3x = 0.0 4180 + -1823.3x + 143.3x2 = 0.0 + -143.3x2 + 143.3x2 4180 + -1823.3x + 143.3x2 = -143.3x2 + 143.3x2 Combine like terms: -143.3x2 + 143.3x2 = 0.0 4180 + -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'. 29.16957432 + -12.72365666x + x2 = 0 Move the constant term to the right: Add '-29.16957432' to each side of the equation. 29.16957432 + -12.72365666x + -29.16957432 + x2 = 0 + -29.16957432 Reorder the terms: 29.16957432 + -29.16957432 + -12.72365666x + x2 = 0 + -29.16957432 Combine like terms: 29.16957432 + -29.16957432 = 0.00000000 0.00000000 + -12.72365666x + x2 = 0 + -29.16957432 -12.72365666x + x2 = 0 + -29.16957432 Combine like terms: 0 + -29.16957432 = -29.16957432 -12.72365666x + x2 = -29.16957432 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 = -29.16957432 + 40.47285970 Reorder the terms: 40.47285970 + -12.72365666x + x2 = -29.16957432 + 40.47285970 Combine like terms: -29.16957432 + 40.47285970 = 11.30328538 40.47285970 + -12.72365666x + x2 = 11.30328538 Factor a perfect square on the left side: (x + -6.36182833)(x + -6.36182833) = 11.30328538 Calculate the square root of the right side: 3.362035898 Break this problem into two subproblems by setting (x + -6.36182833) equal to 3.362035898 and -3.362035898.Subproblem 1
x + -6.36182833 = 3.362035898 Simplifying x + -6.36182833 = 3.362035898 Reorder the terms: -6.36182833 + x = 3.362035898 Solving -6.36182833 + x = 3.362035898 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 = 3.362035898 + 6.36182833 Combine like terms: -6.36182833 + 6.36182833 = 0.00000000 0.00000000 + x = 3.362035898 + 6.36182833 x = 3.362035898 + 6.36182833 Combine like terms: 3.362035898 + 6.36182833 = 9.723864228 x = 9.723864228 Simplifying x = 9.723864228Subproblem 2
x + -6.36182833 = -3.362035898 Simplifying x + -6.36182833 = -3.362035898 Reorder the terms: -6.36182833 + x = -3.362035898 Solving -6.36182833 + x = -3.362035898 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 = -3.362035898 + 6.36182833 Combine like terms: -6.36182833 + 6.36182833 = 0.00000000 0.00000000 + x = -3.362035898 + 6.36182833 x = -3.362035898 + 6.36182833 Combine like terms: -3.362035898 + 6.36182833 = 2.999792432 x = 2.999792432 Simplifying x = 2.999792432Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.723864228, 2.999792432}
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