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Simplifying 5y(y + 2) = 74 + -3y Reorder the terms: 5y(2 + y) = 74 + -3y (2 * 5y + y * 5y) = 74 + -3y (10y + 5y2) = 74 + -3y Solving 10y + 5y2 = 74 + -3y Solving for variable 'y'. Reorder the terms: -74 + 10y + 3y + 5y2 = 74 + -3y + -74 + 3y Combine like terms: 10y + 3y = 13y -74 + 13y + 5y2 = 74 + -3y + -74 + 3y Reorder the terms: -74 + 13y + 5y2 = 74 + -74 + -3y + 3y Combine like terms: 74 + -74 = 0 -74 + 13y + 5y2 = 0 + -3y + 3y -74 + 13y + 5y2 = -3y + 3y Combine like terms: -3y + 3y = 0 -74 + 13y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -14.8 + 2.6y + y2 = 0 Move the constant term to the right: Add '14.8' to each side of the equation. -14.8 + 2.6y + 14.8 + y2 = 0 + 14.8 Reorder the terms: -14.8 + 14.8 + 2.6y + y2 = 0 + 14.8 Combine like terms: -14.8 + 14.8 = 0.0 0.0 + 2.6y + y2 = 0 + 14.8 2.6y + y2 = 0 + 14.8 Combine like terms: 0 + 14.8 = 14.8 2.6y + y2 = 14.8 The y term is 2.6y. Take half its coefficient (1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. 2.6y + 1.69 + y2 = 14.8 + 1.69 Reorder the terms: 1.69 + 2.6y + y2 = 14.8 + 1.69 Combine like terms: 14.8 + 1.69 = 16.49 1.69 + 2.6y + y2 = 16.49 Factor a perfect square on the left side: (y + 1.3)(y + 1.3) = 16.49 Calculate the square root of the right side: 4.060788101 Break this problem into two subproblems by setting (y + 1.3) equal to 4.060788101 and -4.060788101.Subproblem 1
y + 1.3 = 4.060788101 Simplifying y + 1.3 = 4.060788101 Reorder the terms: 1.3 + y = 4.060788101 Solving 1.3 + y = 4.060788101 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + y = 4.060788101 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + y = 4.060788101 + -1.3 y = 4.060788101 + -1.3 Combine like terms: 4.060788101 + -1.3 = 2.760788101 y = 2.760788101 Simplifying y = 2.760788101Subproblem 2
y + 1.3 = -4.060788101 Simplifying y + 1.3 = -4.060788101 Reorder the terms: 1.3 + y = -4.060788101 Solving 1.3 + y = -4.060788101 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + y = -4.060788101 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + y = -4.060788101 + -1.3 y = -4.060788101 + -1.3 Combine like terms: -4.060788101 + -1.3 = -5.360788101 y = -5.360788101 Simplifying y = -5.360788101Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.760788101, -5.360788101}
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