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Simplifying 84000 = 3269x2 + 5199x + 5199 Reorder the terms: 84000 = 5199 + 5199x + 3269x2 Solving 84000 = 5199 + 5199x + 3269x2 Solving for variable 'x'. Combine like terms: 84000 + -5199 = 78801 78801 + -5199x + -3269x2 = 5199 + 5199x + 3269x2 + -5199 + -5199x + -3269x2 Reorder the terms: 78801 + -5199x + -3269x2 = 5199 + -5199 + 5199x + -5199x + 3269x2 + -3269x2 Combine like terms: 5199 + -5199 = 0 78801 + -5199x + -3269x2 = 0 + 5199x + -5199x + 3269x2 + -3269x2 78801 + -5199x + -3269x2 = 5199x + -5199x + 3269x2 + -3269x2 Combine like terms: 5199x + -5199x = 0 78801 + -5199x + -3269x2 = 0 + 3269x2 + -3269x2 78801 + -5199x + -3269x2 = 3269x2 + -3269x2 Combine like terms: 3269x2 + -3269x2 = 0 78801 + -5199x + -3269x2 = 0 Begin completing the square. Divide all terms by -3269 the coefficient of the squared term: Divide each side by '-3269'. -24.10553686 + 1.590394616x + x2 = 0 Move the constant term to the right: Add '24.10553686' to each side of the equation. -24.10553686 + 1.590394616x + 24.10553686 + x2 = 0 + 24.10553686 Reorder the terms: -24.10553686 + 24.10553686 + 1.590394616x + x2 = 0 + 24.10553686 Combine like terms: -24.10553686 + 24.10553686 = 0.00000000 0.00000000 + 1.590394616x + x2 = 0 + 24.10553686 1.590394616x + x2 = 0 + 24.10553686 Combine like terms: 0 + 24.10553686 = 24.10553686 1.590394616x + x2 = 24.10553686 The x term is 1.590394616x. Take half its coefficient (0.795197308). Square it (0.6323387587) and add it to both sides. Add '0.6323387587' to each side of the equation. 1.590394616x + 0.6323387587 + x2 = 24.10553686 + 0.6323387587 Reorder the terms: 0.6323387587 + 1.590394616x + x2 = 24.10553686 + 0.6323387587 Combine like terms: 24.10553686 + 0.6323387587 = 24.7378756187 0.6323387587 + 1.590394616x + x2 = 24.7378756187 Factor a perfect square on the left side: (x + 0.795197308)(x + 0.795197308) = 24.7378756187 Calculate the square root of the right side: 4.97371849 Break this problem into two subproblems by setting (x + 0.795197308) equal to 4.97371849 and -4.97371849.Subproblem 1
x + 0.795197308 = 4.97371849 Simplifying x + 0.795197308 = 4.97371849 Reorder the terms: 0.795197308 + x = 4.97371849 Solving 0.795197308 + x = 4.97371849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.795197308' to each side of the equation. 0.795197308 + -0.795197308 + x = 4.97371849 + -0.795197308 Combine like terms: 0.795197308 + -0.795197308 = 0.000000000 0.000000000 + x = 4.97371849 + -0.795197308 x = 4.97371849 + -0.795197308 Combine like terms: 4.97371849 + -0.795197308 = 4.178521182 x = 4.178521182 Simplifying x = 4.178521182Subproblem 2
x + 0.795197308 = -4.97371849 Simplifying x + 0.795197308 = -4.97371849 Reorder the terms: 0.795197308 + x = -4.97371849 Solving 0.795197308 + x = -4.97371849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.795197308' to each side of the equation. 0.795197308 + -0.795197308 + x = -4.97371849 + -0.795197308 Combine like terms: 0.795197308 + -0.795197308 = 0.000000000 0.000000000 + x = -4.97371849 + -0.795197308 x = -4.97371849 + -0.795197308 Combine like terms: -4.97371849 + -0.795197308 = -5.768915798 x = -5.768915798 Simplifying x = -5.768915798Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.178521182, -5.768915798}
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