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Simplifying y2 + -12y + 33 = 0 Reorder the terms: 33 + -12y + y2 = 0 Solving 33 + -12y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + -12y + -33 + y2 = 0 + -33 Reorder the terms: 33 + -33 + -12y + y2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -12y + y2 = 0 + -33 -12y + y2 = 0 + -33 Combine like terms: 0 + -33 = -33 -12y + y2 = -33 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = -33 + 36 Reorder the terms: 36 + -12y + y2 = -33 + 36 Combine like terms: -33 + 36 = 3 36 + -12y + y2 = 3 Factor a perfect square on the left side: (y + -6)(y + -6) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (y + -6) equal to 1.732050808 and -1.732050808.Subproblem 1
y + -6 = 1.732050808 Simplifying y + -6 = 1.732050808 Reorder the terms: -6 + y = 1.732050808 Solving -6 + y = 1.732050808 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 1.732050808 + 6 Combine like terms: -6 + 6 = 0 0 + y = 1.732050808 + 6 y = 1.732050808 + 6 Combine like terms: 1.732050808 + 6 = 7.732050808 y = 7.732050808 Simplifying y = 7.732050808Subproblem 2
y + -6 = -1.732050808 Simplifying y + -6 = -1.732050808 Reorder the terms: -6 + y = -1.732050808 Solving -6 + y = -1.732050808 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -1.732050808 + 6 Combine like terms: -6 + 6 = 0 0 + y = -1.732050808 + 6 y = -1.732050808 + 6 Combine like terms: -1.732050808 + 6 = 4.267949192 y = 4.267949192 Simplifying y = 4.267949192Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.732050808, 4.267949192}
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