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Simplifying 20y2 + 6y + -17 = 0 Reorder the terms: -17 + 6y + 20y2 = 0 Solving -17 + 6y + 20y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.85 + 0.3y + y2 = 0 Move the constant term to the right: Add '0.85' to each side of the equation. -0.85 + 0.3y + 0.85 + y2 = 0 + 0.85 Reorder the terms: -0.85 + 0.85 + 0.3y + y2 = 0 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + 0.3y + y2 = 0 + 0.85 0.3y + y2 = 0 + 0.85 Combine like terms: 0 + 0.85 = 0.85 0.3y + y2 = 0.85 The y term is 0.3y. 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. 0.3y + 0.0225 + y2 = 0.85 + 0.0225 Reorder the terms: 0.0225 + 0.3y + y2 = 0.85 + 0.0225 Combine like terms: 0.85 + 0.0225 = 0.8725 0.0225 + 0.3y + y2 = 0.8725 Factor a perfect square on the left side: (y + 0.15)(y + 0.15) = 0.8725 Calculate the square root of the right side: 0.934077085 Break this problem into two subproblems by setting (y + 0.15) equal to 0.934077085 and -0.934077085.Subproblem 1
y + 0.15 = 0.934077085 Simplifying y + 0.15 = 0.934077085 Reorder the terms: 0.15 + y = 0.934077085 Solving 0.15 + y = 0.934077085 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + y = 0.934077085 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + y = 0.934077085 + -0.15 y = 0.934077085 + -0.15 Combine like terms: 0.934077085 + -0.15 = 0.784077085 y = 0.784077085 Simplifying y = 0.784077085Subproblem 2
y + 0.15 = -0.934077085 Simplifying y + 0.15 = -0.934077085 Reorder the terms: 0.15 + y = -0.934077085 Solving 0.15 + y = -0.934077085 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + y = -0.934077085 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + y = -0.934077085 + -0.15 y = -0.934077085 + -0.15 Combine like terms: -0.934077085 + -0.15 = -1.084077085 y = -1.084077085 Simplifying y = -1.084077085Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.784077085, -1.084077085}
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