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Simplifying 9x2 + 27x + -16 = 0 Reorder the terms: -16 + 27x + 9x2 = 0 Solving -16 + 27x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + 3x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + 3x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + 3x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + 3x + x2 = 0 + 1.777777778 3x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 3x + x2 = 1.777777778 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 1.777777778 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 1.777777778 + 2.25 Combine like terms: 1.777777778 + 2.25 = 4.027777778 2.25 + 3x + x2 = 4.027777778 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 4.027777778 Calculate the square root of the right side: 2.00693243 Break this problem into two subproblems by setting (x + 1.5) equal to 2.00693243 and -2.00693243.Subproblem 1
x + 1.5 = 2.00693243 Simplifying x + 1.5 = 2.00693243 Reorder the terms: 1.5 + x = 2.00693243 Solving 1.5 + x = 2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.00693243 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.00693243 + -1.5 x = 2.00693243 + -1.5 Combine like terms: 2.00693243 + -1.5 = 0.50693243 x = 0.50693243 Simplifying x = 0.50693243Subproblem 2
x + 1.5 = -2.00693243 Simplifying x + 1.5 = -2.00693243 Reorder the terms: 1.5 + x = -2.00693243 Solving 1.5 + x = -2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.00693243 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.00693243 + -1.5 x = -2.00693243 + -1.5 Combine like terms: -2.00693243 + -1.5 = -3.50693243 x = -3.50693243 Simplifying x = -3.50693243Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.50693243, -3.50693243}
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