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Simplifying y2 + -12y + 8 = 0 Reorder the terms: 8 + -12y + y2 = 0 Solving 8 + -12y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -12y + -8 + y2 = 0 + -8 Reorder the terms: 8 + -8 + -12y + y2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -12y + y2 = 0 + -8 -12y + y2 = 0 + -8 Combine like terms: 0 + -8 = -8 -12y + y2 = -8 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 = -8 + 36 Reorder the terms: 36 + -12y + y2 = -8 + 36 Combine like terms: -8 + 36 = 28 36 + -12y + y2 = 28 Factor a perfect square on the left side: (y + -6)(y + -6) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (y + -6) equal to 5.291502622 and -5.291502622.Subproblem 1
y + -6 = 5.291502622 Simplifying y + -6 = 5.291502622 Reorder the terms: -6 + y = 5.291502622 Solving -6 + y = 5.291502622 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 = 5.291502622 + 6 Combine like terms: -6 + 6 = 0 0 + y = 5.291502622 + 6 y = 5.291502622 + 6 Combine like terms: 5.291502622 + 6 = 11.291502622 y = 11.291502622 Simplifying y = 11.291502622Subproblem 2
y + -6 = -5.291502622 Simplifying y + -6 = -5.291502622 Reorder the terms: -6 + y = -5.291502622 Solving -6 + y = -5.291502622 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 = -5.291502622 + 6 Combine like terms: -6 + 6 = 0 0 + y = -5.291502622 + 6 y = -5.291502622 + 6 Combine like terms: -5.291502622 + 6 = 0.708497378 y = 0.708497378 Simplifying y = 0.708497378Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.291502622, 0.708497378}
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