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Simplifying 9x2 + 27x + -2 = 0 Reorder the terms: -2 + 27x + 9x2 = 0 Solving -2 + 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'. -0.2222222222 + 3x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 3x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 3x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 3x + x2 = 0 + 0.2222222222 3x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 3x + x2 = 0.2222222222 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 = 0.2222222222 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 0.2222222222 + 2.25 Combine like terms: 0.2222222222 + 2.25 = 2.4722222222 2.25 + 3x + x2 = 2.4722222222 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 2.4722222222 Calculate the square root of the right side: 1.572330189 Break this problem into two subproblems by setting (x + 1.5) equal to 1.572330189 and -1.572330189.Subproblem 1
x + 1.5 = 1.572330189 Simplifying x + 1.5 = 1.572330189 Reorder the terms: 1.5 + x = 1.572330189 Solving 1.5 + x = 1.572330189 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 = 1.572330189 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.572330189 + -1.5 x = 1.572330189 + -1.5 Combine like terms: 1.572330189 + -1.5 = 0.072330189 x = 0.072330189 Simplifying x = 0.072330189Subproblem 2
x + 1.5 = -1.572330189 Simplifying x + 1.5 = -1.572330189 Reorder the terms: 1.5 + x = -1.572330189 Solving 1.5 + x = -1.572330189 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 = -1.572330189 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.572330189 + -1.5 x = -1.572330189 + -1.5 Combine like terms: -1.572330189 + -1.5 = -3.072330189 x = -3.072330189 Simplifying x = -3.072330189Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.072330189, -3.072330189}
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