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Simplifying -1y2 = 6y + -1 Reorder the terms: -1y2 = -1 + 6y Solving -1y2 = -1 + 6y Solving for variable 'y'. Reorder the terms: 1 + -6y + -1y2 = -1 + 6y + 1 + -6y Reorder the terms: 1 + -6y + -1y2 = -1 + 1 + 6y + -6y Combine like terms: -1 + 1 = 0 1 + -6y + -1y2 = 0 + 6y + -6y 1 + -6y + -1y2 = 6y + -6y Combine like terms: 6y + -6y = 0 1 + -6y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + 6y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 6y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + 6y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6y + y2 = 0 + 1 6y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 6y + y2 = 1 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 = 1 + 9 Reorder the terms: 9 + 6y + y2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + 6y + y2 = 10 Factor a perfect square on the left side: (y + 3)(y + 3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (y + 3) equal to 3.16227766 and -3.16227766.Subproblem 1
y + 3 = 3.16227766 Simplifying y + 3 = 3.16227766 Reorder the terms: 3 + y = 3.16227766 Solving 3 + y = 3.16227766 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 = 3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + y = 3.16227766 + -3 y = 3.16227766 + -3 Combine like terms: 3.16227766 + -3 = 0.16227766 y = 0.16227766 Simplifying y = 0.16227766Subproblem 2
y + 3 = -3.16227766 Simplifying y + 3 = -3.16227766 Reorder the terms: 3 + y = -3.16227766 Solving 3 + y = -3.16227766 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 = -3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + y = -3.16227766 + -3 y = -3.16227766 + -3 Combine like terms: -3.16227766 + -3 = -6.16227766 y = -6.16227766 Simplifying y = -6.16227766Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.16227766, -6.16227766}
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