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Simplifying 20x2 + -6x + -17 = 0 Reorder the terms: -17 + -6x + 20x2 = 0 Solving -17 + -6x + 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'. -0.85 + -0.3x + x2 = 0 Move the constant term to the right: Add '0.85' to each side of the equation. -0.85 + -0.3x + 0.85 + x2 = 0 + 0.85 Reorder the terms: -0.85 + 0.85 + -0.3x + x2 = 0 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + -0.3x + x2 = 0 + 0.85 -0.3x + x2 = 0 + 0.85 Combine like terms: 0 + 0.85 = 0.85 -0.3x + x2 = 0.85 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 0.85 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 0.85 + 0.0225 Combine like terms: 0.85 + 0.0225 = 0.8725 0.0225 + -0.3x + x2 = 0.8725 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 0.8725 Calculate the square root of the right side: 0.934077085 Break this problem into two subproblems by setting (x + -0.15) equal to 0.934077085 and -0.934077085.Subproblem 1
x + -0.15 = 0.934077085 Simplifying x + -0.15 = 0.934077085 Reorder the terms: -0.15 + x = 0.934077085 Solving -0.15 + x = 0.934077085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 0.934077085 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 0.934077085 + 0.15 x = 0.934077085 + 0.15 Combine like terms: 0.934077085 + 0.15 = 1.084077085 x = 1.084077085 Simplifying x = 1.084077085Subproblem 2
x + -0.15 = -0.934077085 Simplifying x + -0.15 = -0.934077085 Reorder the terms: -0.15 + x = -0.934077085 Solving -0.15 + x = -0.934077085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -0.934077085 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -0.934077085 + 0.15 x = -0.934077085 + 0.15 Combine like terms: -0.934077085 + 0.15 = -0.784077085 x = -0.784077085 Simplifying x = -0.784077085Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.084077085, -0.784077085}
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