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Simplifying 3x2 + 54x + -730 = 0 Reorder the terms: -730 + 54x + 3x2 = 0 Solving -730 + 54x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -243.3333333 + 18x + x2 = 0 Move the constant term to the right: Add '243.3333333' to each side of the equation. -243.3333333 + 18x + 243.3333333 + x2 = 0 + 243.3333333 Reorder the terms: -243.3333333 + 243.3333333 + 18x + x2 = 0 + 243.3333333 Combine like terms: -243.3333333 + 243.3333333 = 0.0000000 0.0000000 + 18x + x2 = 0 + 243.3333333 18x + x2 = 0 + 243.3333333 Combine like terms: 0 + 243.3333333 = 243.3333333 18x + x2 = 243.3333333 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 243.3333333 + 81 Reorder the terms: 81 + 18x + x2 = 243.3333333 + 81 Combine like terms: 243.3333333 + 81 = 324.3333333 81 + 18x + x2 = 324.3333333 Factor a perfect square on the left side: (x + 9)(x + 9) = 324.3333333 Calculate the square root of the right side: 18.009256878 Break this problem into two subproblems by setting (x + 9) equal to 18.009256878 and -18.009256878.Subproblem 1
x + 9 = 18.009256878 Simplifying x + 9 = 18.009256878 Reorder the terms: 9 + x = 18.009256878 Solving 9 + x = 18.009256878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 18.009256878 + -9 Combine like terms: 9 + -9 = 0 0 + x = 18.009256878 + -9 x = 18.009256878 + -9 Combine like terms: 18.009256878 + -9 = 9.009256878 x = 9.009256878 Simplifying x = 9.009256878Subproblem 2
x + 9 = -18.009256878 Simplifying x + 9 = -18.009256878 Reorder the terms: 9 + x = -18.009256878 Solving 9 + x = -18.009256878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -18.009256878 + -9 Combine like terms: 9 + -9 = 0 0 + x = -18.009256878 + -9 x = -18.009256878 + -9 Combine like terms: -18.009256878 + -9 = -27.009256878 x = -27.009256878 Simplifying x = -27.009256878Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.009256878, -27.009256878}
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