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Simplifying 108x2 + 722x + 3793 = 27000 Reorder the terms: 3793 + 722x + 108x2 = 27000 Solving 3793 + 722x + 108x2 = 27000 Solving for variable 'x'. Reorder the terms: 3793 + -27000 + 722x + 108x2 = 27000 + -27000 Combine like terms: 3793 + -27000 = -23207 -23207 + 722x + 108x2 = 27000 + -27000 Combine like terms: 27000 + -27000 = 0 -23207 + 722x + 108x2 = 0 Begin completing the square. Divide all terms by 108 the coefficient of the squared term: Divide each side by '108'. -214.8796296 + 6.685185185x + x2 = 0 Move the constant term to the right: Add '214.8796296' to each side of the equation. -214.8796296 + 6.685185185x + 214.8796296 + x2 = 0 + 214.8796296 Reorder the terms: -214.8796296 + 214.8796296 + 6.685185185x + x2 = 0 + 214.8796296 Combine like terms: -214.8796296 + 214.8796296 = 0.0000000 0.0000000 + 6.685185185x + x2 = 0 + 214.8796296 6.685185185x + x2 = 0 + 214.8796296 Combine like terms: 0 + 214.8796296 = 214.8796296 6.685185185x + x2 = 214.8796296 The x term is 6.685185185x. Take half its coefficient (3.342592593). Square it (11.17292524) and add it to both sides. Add '11.17292524' to each side of the equation. 6.685185185x + 11.17292524 + x2 = 214.8796296 + 11.17292524 Reorder the terms: 11.17292524 + 6.685185185x + x2 = 214.8796296 + 11.17292524 Combine like terms: 214.8796296 + 11.17292524 = 226.05255484 11.17292524 + 6.685185185x + x2 = 226.05255484 Factor a perfect square on the left side: (x + 3.342592593)(x + 3.342592593) = 226.05255484 Calculate the square root of the right side: 15.035044225 Break this problem into two subproblems by setting (x + 3.342592593) equal to 15.035044225 and -15.035044225.Subproblem 1
x + 3.342592593 = 15.035044225 Simplifying x + 3.342592593 = 15.035044225 Reorder the terms: 3.342592593 + x = 15.035044225 Solving 3.342592593 + x = 15.035044225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.342592593' to each side of the equation. 3.342592593 + -3.342592593 + x = 15.035044225 + -3.342592593 Combine like terms: 3.342592593 + -3.342592593 = 0.000000000 0.000000000 + x = 15.035044225 + -3.342592593 x = 15.035044225 + -3.342592593 Combine like terms: 15.035044225 + -3.342592593 = 11.692451632 x = 11.692451632 Simplifying x = 11.692451632Subproblem 2
x + 3.342592593 = -15.035044225 Simplifying x + 3.342592593 = -15.035044225 Reorder the terms: 3.342592593 + x = -15.035044225 Solving 3.342592593 + x = -15.035044225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.342592593' to each side of the equation. 3.342592593 + -3.342592593 + x = -15.035044225 + -3.342592593 Combine like terms: 3.342592593 + -3.342592593 = 0.000000000 0.000000000 + x = -15.035044225 + -3.342592593 x = -15.035044225 + -3.342592593 Combine like terms: -15.035044225 + -3.342592593 = -18.377636818 x = -18.377636818 Simplifying x = -18.377636818Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.692451632, -18.377636818}
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