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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 = 3.1725 2.7225 + -3.3x + x2 = 3.1725 Factor a perfect square on the left side: (x + -1.65)(x + -1.65) = 3.1725 Calculate the square root of the right side: 1.781151313 Break this problem into two subproblems by setting (x + -1.65) equal to 1.781151313 and -1.781151313.Subproblem 1
x + -1.65 = 1.781151313 Simplifying x + -1.65 = 1.781151313 Reorder the terms: -1.65 + x = 1.781151313 Solving -1.65 + x = 1.781151313 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 = 1.781151313 + 1.65 Combine like terms: -1.65 + 1.65 = 0.00 0.00 + x = 1.781151313 + 1.65 x = 1.781151313 + 1.65 Combine like terms: 1.781151313 + 1.65 = 3.431151313 x = 3.431151313 Simplifying x = 3.431151313Subproblem 2
x + -1.65 = -1.781151313 Simplifying x + -1.65 = -1.781151313 Reorder the terms: -1.65 + x = -1.781151313 Solving -1.65 + x = -1.781151313 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 = -1.781151313 + 1.65 Combine like terms: -1.65 + 1.65 = 0.00 0.00 + x = -1.781151313 + 1.65 x = -1.781151313 + 1.65 Combine like terms: -1.781151313 + 1.65 = -0.131151313 x = -0.131151313 Simplifying x = -0.131151313Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.431151313, -0.131151313}
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