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Simplifying 27.92x2 + 1046.86x + -18410 = 0 Reorder the terms: -18410 + 1046.86x + 27.92x2 = 0 Solving -18410 + 1046.86x + 27.92x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27.92 the coefficient of the squared term: Divide each side by '27.92'. -659.3839542 + 37.49498567x + x2 = 0 Move the constant term to the right: Add '659.3839542' to each side of the equation. -659.3839542 + 37.49498567x + 659.3839542 + x2 = 0 + 659.3839542 Reorder the terms: -659.3839542 + 659.3839542 + 37.49498567x + x2 = 0 + 659.3839542 Combine like terms: -659.3839542 + 659.3839542 = 0.0000000 0.0000000 + 37.49498567x + x2 = 0 + 659.3839542 37.49498567x + x2 = 0 + 659.3839542 Combine like terms: 0 + 659.3839542 = 659.3839542 37.49498567x + x2 = 659.3839542 The x term is 37.49498567x. Take half its coefficient (18.74749284). Square it (351.4684878) and add it to both sides. Add '351.4684878' to each side of the equation. 37.49498567x + 351.4684878 + x2 = 659.3839542 + 351.4684878 Reorder the terms: 351.4684878 + 37.49498567x + x2 = 659.3839542 + 351.4684878 Combine like terms: 659.3839542 + 351.4684878 = 1010.852442 351.4684878 + 37.49498567x + x2 = 1010.852442 Factor a perfect square on the left side: (x + 18.74749284)(x + 18.74749284) = 1010.852442 Calculate the square root of the right side: 31.793905737 Break this problem into two subproblems by setting (x + 18.74749284) equal to 31.793905737 and -31.793905737.Subproblem 1
x + 18.74749284 = 31.793905737 Simplifying x + 18.74749284 = 31.793905737 Reorder the terms: 18.74749284 + x = 31.793905737 Solving 18.74749284 + x = 31.793905737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.74749284' to each side of the equation. 18.74749284 + -18.74749284 + x = 31.793905737 + -18.74749284 Combine like terms: 18.74749284 + -18.74749284 = 0.00000000 0.00000000 + x = 31.793905737 + -18.74749284 x = 31.793905737 + -18.74749284 Combine like terms: 31.793905737 + -18.74749284 = 13.046412897 x = 13.046412897 Simplifying x = 13.046412897Subproblem 2
x + 18.74749284 = -31.793905737 Simplifying x + 18.74749284 = -31.793905737 Reorder the terms: 18.74749284 + x = -31.793905737 Solving 18.74749284 + x = -31.793905737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.74749284' to each side of the equation. 18.74749284 + -18.74749284 + x = -31.793905737 + -18.74749284 Combine like terms: 18.74749284 + -18.74749284 = 0.00000000 0.00000000 + x = -31.793905737 + -18.74749284 x = -31.793905737 + -18.74749284 Combine like terms: -31.793905737 + -18.74749284 = -50.541398577 x = -50.541398577 Simplifying x = -50.541398577Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.046412897, -50.541398577}
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