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Simplifying 3x2 + 27x + -8.1 = 0 Reorder the terms: -8.1 + 27x + 3x2 = 0 Solving -8.1 + 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'. -2.7 + 9x + x2 = 0 Move the constant term to the right: Add '2.7' to each side of the equation. -2.7 + 9x + 2.7 + x2 = 0 + 2.7 Reorder the terms: -2.7 + 2.7 + 9x + x2 = 0 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + 9x + x2 = 0 + 2.7 9x + x2 = 0 + 2.7 Combine like terms: 0 + 2.7 = 2.7 9x + x2 = 2.7 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 = 2.7 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 2.7 + 20.25 Combine like terms: 2.7 + 20.25 = 22.95 20.25 + 9x + x2 = 22.95 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 22.95 Calculate the square root of the right side: 4.790615827 Break this problem into two subproblems by setting (x + 4.5) equal to 4.790615827 and -4.790615827.Subproblem 1
x + 4.5 = 4.790615827 Simplifying x + 4.5 = 4.790615827 Reorder the terms: 4.5 + x = 4.790615827 Solving 4.5 + x = 4.790615827 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 = 4.790615827 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.790615827 + -4.5 x = 4.790615827 + -4.5 Combine like terms: 4.790615827 + -4.5 = 0.290615827 x = 0.290615827 Simplifying x = 0.290615827Subproblem 2
x + 4.5 = -4.790615827 Simplifying x + 4.5 = -4.790615827 Reorder the terms: 4.5 + x = -4.790615827 Solving 4.5 + x = -4.790615827 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 = -4.790615827 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.790615827 + -4.5 x = -4.790615827 + -4.5 Combine like terms: -4.790615827 + -4.5 = -9.290615827 x = -9.290615827 Simplifying x = -9.290615827Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.290615827, -9.290615827}
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