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Simplifying -1y2 + -6y + 3 = 0 Reorder the terms: 3 + -6y + -1y2 = 0 Solving 3 + -6y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 6y + y2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 6y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + 6y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6y + y2 = 0 + 3 6y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 6y + y2 = 3 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 = 3 + 9 Reorder the terms: 9 + 6y + y2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + 6y + y2 = 12 Factor a perfect square on the left side: (y + 3)(y + 3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (y + 3) equal to 3.464101615 and -3.464101615.Subproblem 1
y + 3 = 3.464101615 Simplifying y + 3 = 3.464101615 Reorder the terms: 3 + y = 3.464101615 Solving 3 + y = 3.464101615 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 = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + y = 3.464101615 + -3 y = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 y = 0.464101615 Simplifying y = 0.464101615Subproblem 2
y + 3 = -3.464101615 Simplifying y + 3 = -3.464101615 Reorder the terms: 3 + y = -3.464101615 Solving 3 + y = -3.464101615 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 = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + y = -3.464101615 + -3 y = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 y = -6.464101615 Simplifying y = -6.464101615Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.464101615, -6.464101615}
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