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Simplifying y(3 + 0.5y) = 140 (3 * y + 0.5y * y) = 140 (3y + 0.5y2) = 140 Solving 3y + 0.5y2 = 140 Solving for variable 'y'. Reorder the terms: -140 + 3y + 0.5y2 = 140 + -140 Combine like terms: 140 + -140 = 0 -140 + 3y + 0.5y2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -280 + 6y + y2 = 0 Move the constant term to the right: Add '280' to each side of the equation. -280 + 6y + 280 + y2 = 0 + 280 Reorder the terms: -280 + 280 + 6y + y2 = 0 + 280 Combine like terms: -280 + 280 = 0 0 + 6y + y2 = 0 + 280 6y + y2 = 0 + 280 Combine like terms: 0 + 280 = 280 6y + y2 = 280 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = 280 + 9 Reorder the terms: 9 + 6y + y2 = 280 + 9 Combine like terms: 280 + 9 = 289 9 + 6y + y2 = 289 Factor a perfect square on the left side: (y + 3)(y + 3) = 289 Calculate the square root of the right side: 17 Break this problem into two subproblems by setting (y + 3) equal to 17 and -17.Subproblem 1
y + 3 = 17 Simplifying y + 3 = 17 Reorder the terms: 3 + y = 17 Solving 3 + y = 17 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 17 + -3 Combine like terms: 3 + -3 = 0 0 + y = 17 + -3 y = 17 + -3 Combine like terms: 17 + -3 = 14 y = 14 Simplifying y = 14Subproblem 2
y + 3 = -17 Simplifying y + 3 = -17 Reorder the terms: 3 + y = -17 Solving 3 + y = -17 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -17 + -3 Combine like terms: 3 + -3 = 0 0 + y = -17 + -3 y = -17 + -3 Combine like terms: -17 + -3 = -20 y = -20 Simplifying y = -20Solution
The solution to the problem is based on the solutions from the subproblems. y = {14, -20}
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