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Simplifying 5y(y + 2) = 54 Reorder the terms: 5y(2 + y) = 54 (2 * 5y + y * 5y) = 54 (10y + 5y2) = 54 Solving 10y + 5y2 = 54 Solving for variable 'y'. Reorder the terms: -54 + 10y + 5y2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 10y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10.8 + 2y + y2 = 0 Move the constant term to the right: Add '10.8' to each side of the equation. -10.8 + 2y + 10.8 + y2 = 0 + 10.8 Reorder the terms: -10.8 + 10.8 + 2y + y2 = 0 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + 2y + y2 = 0 + 10.8 2y + y2 = 0 + 10.8 Combine like terms: 0 + 10.8 = 10.8 2y + y2 = 10.8 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 10.8 + 1 Reorder the terms: 1 + 2y + y2 = 10.8 + 1 Combine like terms: 10.8 + 1 = 11.8 1 + 2y + y2 = 11.8 Factor a perfect square on the left side: (y + 1)(y + 1) = 11.8 Calculate the square root of the right side: 3.435112807 Break this problem into two subproblems by setting (y + 1) equal to 3.435112807 and -3.435112807.Subproblem 1
y + 1 = 3.435112807 Simplifying y + 1 = 3.435112807 Reorder the terms: 1 + y = 3.435112807 Solving 1 + y = 3.435112807 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 3.435112807 + -1 Combine like terms: 1 + -1 = 0 0 + y = 3.435112807 + -1 y = 3.435112807 + -1 Combine like terms: 3.435112807 + -1 = 2.435112807 y = 2.435112807 Simplifying y = 2.435112807Subproblem 2
y + 1 = -3.435112807 Simplifying y + 1 = -3.435112807 Reorder the terms: 1 + y = -3.435112807 Solving 1 + y = -3.435112807 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -3.435112807 + -1 Combine like terms: 1 + -1 = 0 0 + y = -3.435112807 + -1 y = -3.435112807 + -1 Combine like terms: -3.435112807 + -1 = -4.435112807 y = -4.435112807 Simplifying y = -4.435112807Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.435112807, -4.435112807}
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