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Simplifying -1y2 = 6y + -2 Reorder the terms: -1y2 = -2 + 6y Solving -1y2 = -2 + 6y Solving for variable 'y'. Reorder the terms: 2 + -6y + -1y2 = -2 + 6y + 2 + -6y Reorder the terms: 2 + -6y + -1y2 = -2 + 2 + 6y + -6y Combine like terms: -2 + 2 = 0 2 + -6y + -1y2 = 0 + 6y + -6y 2 + -6y + -1y2 = 6y + -6y Combine like terms: 6y + -6y = 0 2 + -6y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 6y + y2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 6y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + 6y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6y + y2 = 0 + 2 6y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 6y + y2 = 2 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 = 2 + 9 Reorder the terms: 9 + 6y + y2 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + 6y + y2 = 11 Factor a perfect square on the left side: (y + 3)(y + 3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (y + 3) equal to 3.31662479 and -3.31662479.Subproblem 1
y + 3 = 3.31662479 Simplifying y + 3 = 3.31662479 Reorder the terms: 3 + y = 3.31662479 Solving 3 + y = 3.31662479 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 = 3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + y = 3.31662479 + -3 y = 3.31662479 + -3 Combine like terms: 3.31662479 + -3 = 0.31662479 y = 0.31662479 Simplifying y = 0.31662479Subproblem 2
y + 3 = -3.31662479 Simplifying y + 3 = -3.31662479 Reorder the terms: 3 + y = -3.31662479 Solving 3 + y = -3.31662479 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 = -3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + y = -3.31662479 + -3 y = -3.31662479 + -3 Combine like terms: -3.31662479 + -3 = -6.31662479 y = -6.31662479 Simplifying y = -6.31662479Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.31662479, -6.31662479}
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