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Simplifying 3x2 + 27x + 59 = 0 Reorder the terms: 59 + 27x + 3x2 = 0 Solving 59 + 27x + 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'. 19.66666667 + 9x + x2 = 0 Move the constant term to the right: Add '-19.66666667' to each side of the equation. 19.66666667 + 9x + -19.66666667 + x2 = 0 + -19.66666667 Reorder the terms: 19.66666667 + -19.66666667 + 9x + x2 = 0 + -19.66666667 Combine like terms: 19.66666667 + -19.66666667 = 0.00000000 0.00000000 + 9x + x2 = 0 + -19.66666667 9x + x2 = 0 + -19.66666667 Combine like terms: 0 + -19.66666667 = -19.66666667 9x + x2 = -19.66666667 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -19.66666667 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -19.66666667 + 20.25 Combine like terms: -19.66666667 + 20.25 = 0.58333333 20.25 + 9x + x2 = 0.58333333 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 0.58333333 Calculate the square root of the right side: 0.763762614 Break this problem into two subproblems by setting (x + 4.5) equal to 0.763762614 and -0.763762614.Subproblem 1
x + 4.5 = 0.763762614 Simplifying x + 4.5 = 0.763762614 Reorder the terms: 4.5 + x = 0.763762614 Solving 4.5 + x = 0.763762614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 0.763762614 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 0.763762614 + -4.5 x = 0.763762614 + -4.5 Combine like terms: 0.763762614 + -4.5 = -3.736237386 x = -3.736237386 Simplifying x = -3.736237386Subproblem 2
x + 4.5 = -0.763762614 Simplifying x + 4.5 = -0.763762614 Reorder the terms: 4.5 + x = -0.763762614 Solving 4.5 + x = -0.763762614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -0.763762614 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -0.763762614 + -4.5 x = -0.763762614 + -4.5 Combine like terms: -0.763762614 + -4.5 = -5.263762614 x = -5.263762614 Simplifying x = -5.263762614Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.736237386, -5.263762614}
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