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Simplifying 20x2 + -66x + 9 = 0 Reorder the terms: 9 + -66x + 20x2 = 0 Solving 9 + -66x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.45 + -3.3x + x2 = 0 Move the constant term to the right: Add '-0.45' to each side of the equation. 0.45 + -3.3x + -0.45 + x2 = 0 + -0.45 Reorder the terms: 0.45 + -0.45 + -3.3x + x2 = 0 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + -3.3x + x2 = 0 + -0.45 -3.3x + x2 = 0 + -0.45 Combine like terms: 0 + -0.45 = -0.45 -3.3x + x2 = -0.45 The x term is -3.3x. Take half its coefficient (-1.65). Square it (2.7225) and add it to both sides. Add '2.7225' to each side of the equation. -3.3x + 2.7225 + x2 = -0.45 + 2.7225 Reorder the terms: 2.7225 + -3.3x + x2 = -0.45 + 2.7225 Combine like terms: -0.45 + 2.7225 = 2.2725 2.7225 + -3.3x + x2 = 2.2725 Factor a perfect square on the left side: (x + -1.65)(x + -1.65) = 2.2725 Calculate the square root of the right side: 1.507481343 Break this problem into two subproblems by setting (x + -1.65) equal to 1.507481343 and -1.507481343.Subproblem 1
x + -1.65 = 1.507481343 Simplifying x + -1.65 = 1.507481343 Reorder the terms: -1.65 + x = 1.507481343 Solving -1.65 + x = 1.507481343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.65' to each side of the equation. -1.65 + 1.65 + x = 1.507481343 + 1.65 Combine like terms: -1.65 + 1.65 = 0.00 0.00 + x = 1.507481343 + 1.65 x = 1.507481343 + 1.65 Combine like terms: 1.507481343 + 1.65 = 3.157481343 x = 3.157481343 Simplifying x = 3.157481343Subproblem 2
x + -1.65 = -1.507481343 Simplifying x + -1.65 = -1.507481343 Reorder the terms: -1.65 + x = -1.507481343 Solving -1.65 + x = -1.507481343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.65' to each side of the equation. -1.65 + 1.65 + x = -1.507481343 + 1.65 Combine like terms: -1.65 + 1.65 = 0.00 0.00 + x = -1.507481343 + 1.65 x = -1.507481343 + 1.65 Combine like terms: -1.507481343 + 1.65 = 0.142518657 x = 0.142518657 Simplifying x = 0.142518657Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.157481343, 0.142518657}
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