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Simplifying 6y(y + 6) = 35 Reorder the terms: 6y(6 + y) = 35 (6 * 6y + y * 6y) = 35 (36y + 6y2) = 35 Solving 36y + 6y2 = 35 Solving for variable 'y'. Reorder the terms: -35 + 36y + 6y2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 36y + 6y2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -5.833333333 + 6y + y2 = 0 Move the constant term to the right: Add '5.833333333' to each side of the equation. -5.833333333 + 6y + 5.833333333 + y2 = 0 + 5.833333333 Reorder the terms: -5.833333333 + 5.833333333 + 6y + y2 = 0 + 5.833333333 Combine like terms: -5.833333333 + 5.833333333 = 0.000000000 0.000000000 + 6y + y2 = 0 + 5.833333333 6y + y2 = 0 + 5.833333333 Combine like terms: 0 + 5.833333333 = 5.833333333 6y + y2 = 5.833333333 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 = 5.833333333 + 9 Reorder the terms: 9 + 6y + y2 = 5.833333333 + 9 Combine like terms: 5.833333333 + 9 = 14.833333333 9 + 6y + y2 = 14.833333333 Factor a perfect square on the left side: (y + 3)(y + 3) = 14.833333333 Calculate the square root of the right side: 3.851406669 Break this problem into two subproblems by setting (y + 3) equal to 3.851406669 and -3.851406669.Subproblem 1
y + 3 = 3.851406669 Simplifying y + 3 = 3.851406669 Reorder the terms: 3 + y = 3.851406669 Solving 3 + y = 3.851406669 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 = 3.851406669 + -3 Combine like terms: 3 + -3 = 0 0 + y = 3.851406669 + -3 y = 3.851406669 + -3 Combine like terms: 3.851406669 + -3 = 0.851406669 y = 0.851406669 Simplifying y = 0.851406669Subproblem 2
y + 3 = -3.851406669 Simplifying y + 3 = -3.851406669 Reorder the terms: 3 + y = -3.851406669 Solving 3 + y = -3.851406669 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 = -3.851406669 + -3 Combine like terms: 3 + -3 = 0 0 + y = -3.851406669 + -3 y = -3.851406669 + -3 Combine like terms: -3.851406669 + -3 = -6.851406669 y = -6.851406669 Simplifying y = -6.851406669Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.851406669, -6.851406669}
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