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Simplifying 12 = y(8 + y) 12 = (8 * y + y * y) 12 = (8y + y2) Solving 12 = 8y + y2 Solving for variable 'y'. Reorder the terms: 12 + -8y + -1y2 = 8y + -8y + y2 + -1y2 Combine like terms: 8y + -8y = 0 12 + -8y + -1y2 = 0 + y2 + -1y2 12 + -8y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 12 + -8y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + 8y + y2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 8y + 12 + y2 = 0 + 12 Reorder the terms: -12 + 12 + 8y + y2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 8y + y2 = 0 + 12 8y + y2 = 0 + 12 Combine like terms: 0 + 12 = 12 8y + y2 = 12 The y term is 8y. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8y + 16 + y2 = 12 + 16 Reorder the terms: 16 + 8y + y2 = 12 + 16 Combine like terms: 12 + 16 = 28 16 + 8y + y2 = 28 Factor a perfect square on the left side: (y + 4)(y + 4) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (y + 4) equal to 5.291502622 and -5.291502622.Subproblem 1
y + 4 = 5.291502622 Simplifying y + 4 = 5.291502622 Reorder the terms: 4 + y = 5.291502622 Solving 4 + y = 5.291502622 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + y = 5.291502622 + -4 y = 5.291502622 + -4 Combine like terms: 5.291502622 + -4 = 1.291502622 y = 1.291502622 Simplifying y = 1.291502622Subproblem 2
y + 4 = -5.291502622 Simplifying y + 4 = -5.291502622 Reorder the terms: 4 + y = -5.291502622 Solving 4 + y = -5.291502622 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = -5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + y = -5.291502622 + -4 y = -5.291502622 + -4 Combine like terms: -5.291502622 + -4 = -9.291502622 y = -9.291502622 Simplifying y = -9.291502622Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.291502622, -9.291502622}
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