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Simplifying 27 = 9(y + -3) + 3y + y2 Reorder the terms: 27 = 9(-3 + y) + 3y + y2 27 = (-3 * 9 + y * 9) + 3y + y2 27 = (-27 + 9y) + 3y + y2 Combine like terms: 9y + 3y = 12y 27 = -27 + 12y + y2 Solving 27 = -27 + 12y + y2 Solving for variable 'y'. Combine like terms: 27 + 27 = 54 54 + -12y + -1y2 = -27 + 12y + y2 + 27 + -12y + -1y2 Reorder the terms: 54 + -12y + -1y2 = -27 + 27 + 12y + -12y + y2 + -1y2 Combine like terms: -27 + 27 = 0 54 + -12y + -1y2 = 0 + 12y + -12y + y2 + -1y2 54 + -12y + -1y2 = 12y + -12y + y2 + -1y2 Combine like terms: 12y + -12y = 0 54 + -12y + -1y2 = 0 + y2 + -1y2 54 + -12y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 54 + -12y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -54 + 12y + y2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + 12y + 54 + y2 = 0 + 54 Reorder the terms: -54 + 54 + 12y + y2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 12y + y2 = 0 + 54 12y + y2 = 0 + 54 Combine like terms: 0 + 54 = 54 12y + y2 = 54 The y term is 12y. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12y + 36 + y2 = 54 + 36 Reorder the terms: 36 + 12y + y2 = 54 + 36 Combine like terms: 54 + 36 = 90 36 + 12y + y2 = 90 Factor a perfect square on the left side: (y + 6)(y + 6) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (y + 6) equal to 9.486832981 and -9.486832981.Subproblem 1
y + 6 = 9.486832981 Simplifying y + 6 = 9.486832981 Reorder the terms: 6 + y = 9.486832981 Solving 6 + y = 9.486832981 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + y = 9.486832981 + -6 Combine like terms: 6 + -6 = 0 0 + y = 9.486832981 + -6 y = 9.486832981 + -6 Combine like terms: 9.486832981 + -6 = 3.486832981 y = 3.486832981 Simplifying y = 3.486832981Subproblem 2
y + 6 = -9.486832981 Simplifying y + 6 = -9.486832981 Reorder the terms: 6 + y = -9.486832981 Solving 6 + y = -9.486832981 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + y = -9.486832981 + -6 Combine like terms: 6 + -6 = 0 0 + y = -9.486832981 + -6 y = -9.486832981 + -6 Combine like terms: -9.486832981 + -6 = -15.486832981 y = -15.486832981 Simplifying y = -15.486832981Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.486832981, -15.486832981}
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