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Simplifying 9x2 + -27x + -20 = 0 Reorder the terms: -20 + -27x + 9x2 = 0 Solving -20 + -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'. -2.222222222 + -3x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + -3x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + -3x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + -3x + x2 = 0 + 2.222222222 -3x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 -3x + x2 = 2.222222222 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 = 2.222222222 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 2.222222222 + 2.25 Combine like terms: 2.222222222 + 2.25 = 4.472222222 2.25 + -3x + x2 = 4.472222222 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 4.472222222 Calculate the square root of the right side: 2.114762923 Break this problem into two subproblems by setting (x + -1.5) equal to 2.114762923 and -2.114762923.Subproblem 1
x + -1.5 = 2.114762923 Simplifying x + -1.5 = 2.114762923 Reorder the terms: -1.5 + x = 2.114762923 Solving -1.5 + x = 2.114762923 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 = 2.114762923 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.114762923 + 1.5 x = 2.114762923 + 1.5 Combine like terms: 2.114762923 + 1.5 = 3.614762923 x = 3.614762923 Simplifying x = 3.614762923Subproblem 2
x + -1.5 = -2.114762923 Simplifying x + -1.5 = -2.114762923 Reorder the terms: -1.5 + x = -2.114762923 Solving -1.5 + x = -2.114762923 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 = -2.114762923 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.114762923 + 1.5 x = -2.114762923 + 1.5 Combine like terms: -2.114762923 + 1.5 = -0.614762923 x = -0.614762923 Simplifying x = -0.614762923Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.614762923, -0.614762923}
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