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Simplifying 3y2 + 6y + -44 = 0 Reorder the terms: -44 + 6y + 3y2 = 0 Solving -44 + 6y + 3y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -14.66666667 + 2y + y2 = 0 Move the constant term to the right: Add '14.66666667' to each side of the equation. -14.66666667 + 2y + 14.66666667 + y2 = 0 + 14.66666667 Reorder the terms: -14.66666667 + 14.66666667 + 2y + y2 = 0 + 14.66666667 Combine like terms: -14.66666667 + 14.66666667 = 0.00000000 0.00000000 + 2y + y2 = 0 + 14.66666667 2y + y2 = 0 + 14.66666667 Combine like terms: 0 + 14.66666667 = 14.66666667 2y + y2 = 14.66666667 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 = 14.66666667 + 1 Reorder the terms: 1 + 2y + y2 = 14.66666667 + 1 Combine like terms: 14.66666667 + 1 = 15.66666667 1 + 2y + y2 = 15.66666667 Factor a perfect square on the left side: (y + 1)(y + 1) = 15.66666667 Calculate the square root of the right side: 3.958114029 Break this problem into two subproblems by setting (y + 1) equal to 3.958114029 and -3.958114029.Subproblem 1
y + 1 = 3.958114029 Simplifying y + 1 = 3.958114029 Reorder the terms: 1 + y = 3.958114029 Solving 1 + y = 3.958114029 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 = 3.958114029 + -1 Combine like terms: 1 + -1 = 0 0 + y = 3.958114029 + -1 y = 3.958114029 + -1 Combine like terms: 3.958114029 + -1 = 2.958114029 y = 2.958114029 Simplifying y = 2.958114029Subproblem 2
y + 1 = -3.958114029 Simplifying y + 1 = -3.958114029 Reorder the terms: 1 + y = -3.958114029 Solving 1 + y = -3.958114029 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 = -3.958114029 + -1 Combine like terms: 1 + -1 = 0 0 + y = -3.958114029 + -1 y = -3.958114029 + -1 Combine like terms: -3.958114029 + -1 = -4.958114029 y = -4.958114029 Simplifying y = -4.958114029Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.958114029, -4.958114029}
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