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Simplifying 11x2 + 150x + -500 = 30000 Reorder the terms: -500 + 150x + 11x2 = 30000 Solving -500 + 150x + 11x2 = 30000 Solving for variable 'x'. Reorder the terms: -500 + -30000 + 150x + 11x2 = 30000 + -30000 Combine like terms: -500 + -30000 = -30500 -30500 + 150x + 11x2 = 30000 + -30000 Combine like terms: 30000 + -30000 = 0 -30500 + 150x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -2772.727273 + 13.63636364x + x2 = 0 Move the constant term to the right: Add '2772.727273' to each side of the equation. -2772.727273 + 13.63636364x + 2772.727273 + x2 = 0 + 2772.727273 Reorder the terms: -2772.727273 + 2772.727273 + 13.63636364x + x2 = 0 + 2772.727273 Combine like terms: -2772.727273 + 2772.727273 = 0.000000 0.000000 + 13.63636364x + x2 = 0 + 2772.727273 13.63636364x + x2 = 0 + 2772.727273 Combine like terms: 0 + 2772.727273 = 2772.727273 13.63636364x + x2 = 2772.727273 The x term is 13.63636364x. Take half its coefficient (6.81818182). Square it (46.48760333) and add it to both sides. Add '46.48760333' to each side of the equation. 13.63636364x + 46.48760333 + x2 = 2772.727273 + 46.48760333 Reorder the terms: 46.48760333 + 13.63636364x + x2 = 2772.727273 + 46.48760333 Combine like terms: 2772.727273 + 46.48760333 = 2819.21487633 46.48760333 + 13.63636364x + x2 = 2819.21487633 Factor a perfect square on the left side: (x + 6.81818182)(x + 6.81818182) = 2819.21487633 Calculate the square root of the right side: 53.096279308 Break this problem into two subproblems by setting (x + 6.81818182) equal to 53.096279308 and -53.096279308.Subproblem 1
x + 6.81818182 = 53.096279308 Simplifying x + 6.81818182 = 53.096279308 Reorder the terms: 6.81818182 + x = 53.096279308 Solving 6.81818182 + x = 53.096279308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.81818182' to each side of the equation. 6.81818182 + -6.81818182 + x = 53.096279308 + -6.81818182 Combine like terms: 6.81818182 + -6.81818182 = 0.00000000 0.00000000 + x = 53.096279308 + -6.81818182 x = 53.096279308 + -6.81818182 Combine like terms: 53.096279308 + -6.81818182 = 46.278097488 x = 46.278097488 Simplifying x = 46.278097488Subproblem 2
x + 6.81818182 = -53.096279308 Simplifying x + 6.81818182 = -53.096279308 Reorder the terms: 6.81818182 + x = -53.096279308 Solving 6.81818182 + x = -53.096279308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.81818182' to each side of the equation. 6.81818182 + -6.81818182 + x = -53.096279308 + -6.81818182 Combine like terms: 6.81818182 + -6.81818182 = 0.00000000 0.00000000 + x = -53.096279308 + -6.81818182 x = -53.096279308 + -6.81818182 Combine like terms: -53.096279308 + -6.81818182 = -59.914461128 x = -59.914461128 Simplifying x = -59.914461128Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.278097488, -59.914461128}
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