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Simplifying 3x2 + 27x + 55 = 0 Reorder the terms: 55 + 27x + 3x2 = 0 Solving 55 + 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'. 18.33333333 + 9x + x2 = 0 Move the constant term to the right: Add '-18.33333333' to each side of the equation. 18.33333333 + 9x + -18.33333333 + x2 = 0 + -18.33333333 Reorder the terms: 18.33333333 + -18.33333333 + 9x + x2 = 0 + -18.33333333 Combine like terms: 18.33333333 + -18.33333333 = 0.00000000 0.00000000 + 9x + x2 = 0 + -18.33333333 9x + x2 = 0 + -18.33333333 Combine like terms: 0 + -18.33333333 = -18.33333333 9x + x2 = -18.33333333 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 = -18.33333333 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -18.33333333 + 20.25 Combine like terms: -18.33333333 + 20.25 = 1.91666667 20.25 + 9x + x2 = 1.91666667 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 1.91666667 Calculate the square root of the right side: 1.384437312 Break this problem into two subproblems by setting (x + 4.5) equal to 1.384437312 and -1.384437312.Subproblem 1
x + 4.5 = 1.384437312 Simplifying x + 4.5 = 1.384437312 Reorder the terms: 4.5 + x = 1.384437312 Solving 4.5 + x = 1.384437312 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 = 1.384437312 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 1.384437312 + -4.5 x = 1.384437312 + -4.5 Combine like terms: 1.384437312 + -4.5 = -3.115562688 x = -3.115562688 Simplifying x = -3.115562688Subproblem 2
x + 4.5 = -1.384437312 Simplifying x + 4.5 = -1.384437312 Reorder the terms: 4.5 + x = -1.384437312 Solving 4.5 + x = -1.384437312 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 = -1.384437312 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -1.384437312 + -4.5 x = -1.384437312 + -4.5 Combine like terms: -1.384437312 + -4.5 = -5.884437312 x = -5.884437312 Simplifying x = -5.884437312Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.115562688, -5.884437312}
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