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Simplifying 12500 = -143.3x2 + 1823.3x + 6820 Reorder the terms: 12500 = 6820 + 1823.3x + -143.3x2 Solving 12500 = 6820 + 1823.3x + -143.3x2 Solving for variable 'x'. Combine like terms: 12500 + -6820 = 5680 5680 + -1823.3x + 143.3x2 = 6820 + 1823.3x + -143.3x2 + -6820 + -1823.3x + 143.3x2 Reorder the terms: 5680 + -1823.3x + 143.3x2 = 6820 + -6820 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2 Combine like terms: 6820 + -6820 = 0 5680 + -1823.3x + 143.3x2 = 0 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2 5680 + -1823.3x + 143.3x2 = 1823.3x + -1823.3x + -143.3x2 + 143.3x2 Combine like terms: 1823.3x + -1823.3x = 0.0 5680 + -1823.3x + 143.3x2 = 0.0 + -143.3x2 + 143.3x2 5680 + -1823.3x + 143.3x2 = -143.3x2 + 143.3x2 Combine like terms: -143.3x2 + 143.3x2 = 0.0 5680 + -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'. 39.63712491 + -12.72365666x + x2 = 0 Move the constant term to the right: Add '-39.63712491' to each side of the equation. 39.63712491 + -12.72365666x + -39.63712491 + x2 = 0 + -39.63712491 Reorder the terms: 39.63712491 + -39.63712491 + -12.72365666x + x2 = 0 + -39.63712491 Combine like terms: 39.63712491 + -39.63712491 = 0.00000000 0.00000000 + -12.72365666x + x2 = 0 + -39.63712491 -12.72365666x + x2 = 0 + -39.63712491 Combine like terms: 0 + -39.63712491 = -39.63712491 -12.72365666x + x2 = -39.63712491 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 = -39.63712491 + 40.47285970 Reorder the terms: 40.47285970 + -12.72365666x + x2 = -39.63712491 + 40.47285970 Combine like terms: -39.63712491 + 40.47285970 = 0.83573479 40.47285970 + -12.72365666x + x2 = 0.83573479 Factor a perfect square on the left side: (x + -6.36182833)(x + -6.36182833) = 0.83573479 Calculate the square root of the right side: 0.914185315 Break this problem into two subproblems by setting (x + -6.36182833) equal to 0.914185315 and -0.914185315.Subproblem 1
x + -6.36182833 = 0.914185315 Simplifying x + -6.36182833 = 0.914185315 Reorder the terms: -6.36182833 + x = 0.914185315 Solving -6.36182833 + x = 0.914185315 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 = 0.914185315 + 6.36182833 Combine like terms: -6.36182833 + 6.36182833 = 0.00000000 0.00000000 + x = 0.914185315 + 6.36182833 x = 0.914185315 + 6.36182833 Combine like terms: 0.914185315 + 6.36182833 = 7.276013645 x = 7.276013645 Simplifying x = 7.276013645Subproblem 2
x + -6.36182833 = -0.914185315 Simplifying x + -6.36182833 = -0.914185315 Reorder the terms: -6.36182833 + x = -0.914185315 Solving -6.36182833 + x = -0.914185315 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 = -0.914185315 + 6.36182833 Combine like terms: -6.36182833 + 6.36182833 = 0.00000000 0.00000000 + x = -0.914185315 + 6.36182833 x = -0.914185315 + 6.36182833 Combine like terms: -0.914185315 + 6.36182833 = 5.447643015 x = 5.447643015 Simplifying x = 5.447643015Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.276013645, 5.447643015}
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