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Simplifying 8.4932x2 + -61.926x + 685.82 = 20000 Reorder the terms: 685.82 + -61.926x + 8.4932x2 = 20000 Solving 685.82 + -61.926x + 8.4932x2 = 20000 Solving for variable 'x'. Reorder the terms: 685.82 + -20000 + -61.926x + 8.4932x2 = 20000 + -20000 Combine like terms: 685.82 + -20000 = -19314.18 -19314.18 + -61.926x + 8.4932x2 = 20000 + -20000 Combine like terms: 20000 + -20000 = 0 -19314.18 + -61.926x + 8.4932x2 = 0 Begin completing the square. Divide all terms by 8.4932 the coefficient of the squared term: Divide each side by '8.4932'. -2274.075731 + -7.291244761x + x2 = 0 Move the constant term to the right: Add '2274.075731' to each side of the equation. -2274.075731 + -7.291244761x + 2274.075731 + x2 = 0 + 2274.075731 Reorder the terms: -2274.075731 + 2274.075731 + -7.291244761x + x2 = 0 + 2274.075731 Combine like terms: -2274.075731 + 2274.075731 = 0.000000 0.000000 + -7.291244761x + x2 = 0 + 2274.075731 -7.291244761x + x2 = 0 + 2274.075731 Combine like terms: 0 + 2274.075731 = 2274.075731 -7.291244761x + x2 = 2274.075731 The x term is -7.291244761x. Take half its coefficient (-3.645622381). Square it (13.29056254) and add it to both sides. Add '13.29056254' to each side of the equation. -7.291244761x + 13.29056254 + x2 = 2274.075731 + 13.29056254 Reorder the terms: 13.29056254 + -7.291244761x + x2 = 2274.075731 + 13.29056254 Combine like terms: 2274.075731 + 13.29056254 = 2287.36629354 13.29056254 + -7.291244761x + x2 = 2287.36629354 Factor a perfect square on the left side: (x + -3.645622381)(x + -3.645622381) = 2287.36629354 Calculate the square root of the right side: 47.826418364 Break this problem into two subproblems by setting (x + -3.645622381) equal to 47.826418364 and -47.826418364.Subproblem 1
x + -3.645622381 = 47.826418364 Simplifying x + -3.645622381 = 47.826418364 Reorder the terms: -3.645622381 + x = 47.826418364 Solving -3.645622381 + x = 47.826418364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.645622381' to each side of the equation. -3.645622381 + 3.645622381 + x = 47.826418364 + 3.645622381 Combine like terms: -3.645622381 + 3.645622381 = 0.000000000 0.000000000 + x = 47.826418364 + 3.645622381 x = 47.826418364 + 3.645622381 Combine like terms: 47.826418364 + 3.645622381 = 51.472040745 x = 51.472040745 Simplifying x = 51.472040745Subproblem 2
x + -3.645622381 = -47.826418364 Simplifying x + -3.645622381 = -47.826418364 Reorder the terms: -3.645622381 + x = -47.826418364 Solving -3.645622381 + x = -47.826418364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.645622381' to each side of the equation. -3.645622381 + 3.645622381 + x = -47.826418364 + 3.645622381 Combine like terms: -3.645622381 + 3.645622381 = 0.000000000 0.000000000 + x = -47.826418364 + 3.645622381 x = -47.826418364 + 3.645622381 Combine like terms: -47.826418364 + 3.645622381 = -44.180795983 x = -44.180795983 Simplifying x = -44.180795983Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.472040745, -44.180795983}
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