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Simplifying 3x2 + 54x + -104 = 0 Reorder the terms: -104 + 54x + 3x2 = 0 Solving -104 + 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'. -34.66666667 + 18x + x2 = 0 Move the constant term to the right: Add '34.66666667' to each side of the equation. -34.66666667 + 18x + 34.66666667 + x2 = 0 + 34.66666667 Reorder the terms: -34.66666667 + 34.66666667 + 18x + x2 = 0 + 34.66666667 Combine like terms: -34.66666667 + 34.66666667 = 0.00000000 0.00000000 + 18x + x2 = 0 + 34.66666667 18x + x2 = 0 + 34.66666667 Combine like terms: 0 + 34.66666667 = 34.66666667 18x + x2 = 34.66666667 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 = 34.66666667 + 81 Reorder the terms: 81 + 18x + x2 = 34.66666667 + 81 Combine like terms: 34.66666667 + 81 = 115.66666667 81 + 18x + x2 = 115.66666667 Factor a perfect square on the left side: (x + 9)(x + 9) = 115.66666667 Calculate the square root of the right side: 10.75484387 Break this problem into two subproblems by setting (x + 9) equal to 10.75484387 and -10.75484387.Subproblem 1
x + 9 = 10.75484387 Simplifying x + 9 = 10.75484387 Reorder the terms: 9 + x = 10.75484387 Solving 9 + x = 10.75484387 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 = 10.75484387 + -9 Combine like terms: 9 + -9 = 0 0 + x = 10.75484387 + -9 x = 10.75484387 + -9 Combine like terms: 10.75484387 + -9 = 1.75484387 x = 1.75484387 Simplifying x = 1.75484387Subproblem 2
x + 9 = -10.75484387 Simplifying x + 9 = -10.75484387 Reorder the terms: 9 + x = -10.75484387 Solving 9 + x = -10.75484387 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 = -10.75484387 + -9 Combine like terms: 9 + -9 = 0 0 + x = -10.75484387 + -9 x = -10.75484387 + -9 Combine like terms: -10.75484387 + -9 = -19.75484387 x = -19.75484387 Simplifying x = -19.75484387Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.75484387, -19.75484387}
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