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Simplifying y * y + 6y + -9 = 0 Multiply y * y y2 + 6y + -9 = 0 Reorder the terms: -9 + 6y + y2 = 0 Solving -9 + 6y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 6y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + 6y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 6y + y2 = 0 + 9 6y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 6y + y2 = 9 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 = 9 + 9 Reorder the terms: 9 + 6y + y2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + 6y + y2 = 18 Factor a perfect square on the left side: (y + 3)(y + 3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (y + 3) equal to 4.242640687 and -4.242640687.Subproblem 1
y + 3 = 4.242640687 Simplifying y + 3 = 4.242640687 Reorder the terms: 3 + y = 4.242640687 Solving 3 + y = 4.242640687 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 = 4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + y = 4.242640687 + -3 y = 4.242640687 + -3 Combine like terms: 4.242640687 + -3 = 1.242640687 y = 1.242640687 Simplifying y = 1.242640687Subproblem 2
y + 3 = -4.242640687 Simplifying y + 3 = -4.242640687 Reorder the terms: 3 + y = -4.242640687 Solving 3 + y = -4.242640687 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 = -4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + y = -4.242640687 + -3 y = -4.242640687 + -3 Combine like terms: -4.242640687 + -3 = -7.242640687 y = -7.242640687 Simplifying y = -7.242640687Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.242640687, -7.242640687}
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