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Simplifying 1 = (y + -3)(y + -6) Reorder the terms: 1 = (-3 + y)(y + -6) Reorder the terms: 1 = (-3 + y)(-6 + y) Multiply (-3 + y) * (-6 + y) 1 = (-3(-6 + y) + y(-6 + y)) 1 = ((-6 * -3 + y * -3) + y(-6 + y)) 1 = ((18 + -3y) + y(-6 + y)) 1 = (18 + -3y + (-6 * y + y * y)) 1 = (18 + -3y + (-6y + y2)) Combine like terms: -3y + -6y = -9y 1 = (18 + -9y + y2) Solving 1 = 18 + -9y + y2 Solving for variable 'y'. Combine like terms: 1 + -18 = -17 -17 + 9y + -1y2 = 18 + -9y + y2 + -18 + 9y + -1y2 Reorder the terms: -17 + 9y + -1y2 = 18 + -18 + -9y + 9y + y2 + -1y2 Combine like terms: 18 + -18 = 0 -17 + 9y + -1y2 = 0 + -9y + 9y + y2 + -1y2 -17 + 9y + -1y2 = -9y + 9y + y2 + -1y2 Combine like terms: -9y + 9y = 0 -17 + 9y + -1y2 = 0 + y2 + -1y2 -17 + 9y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -17 + 9y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 17 + -9y + y2 = 0 Move the constant term to the right: Add '-17' to each side of the equation. 17 + -9y + -17 + y2 = 0 + -17 Reorder the terms: 17 + -17 + -9y + y2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -9y + y2 = 0 + -17 -9y + y2 = 0 + -17 Combine like terms: 0 + -17 = -17 -9y + y2 = -17 The y term is -9y. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9y + 20.25 + y2 = -17 + 20.25 Reorder the terms: 20.25 + -9y + y2 = -17 + 20.25 Combine like terms: -17 + 20.25 = 3.25 20.25 + -9y + y2 = 3.25 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (y + -4.5) equal to 1.802775638 and -1.802775638.Subproblem 1
y + -4.5 = 1.802775638 Simplifying y + -4.5 = 1.802775638 Reorder the terms: -4.5 + y = 1.802775638 Solving -4.5 + y = 1.802775638 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = 1.802775638 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 1.802775638 + 4.5 y = 1.802775638 + 4.5 Combine like terms: 1.802775638 + 4.5 = 6.302775638 y = 6.302775638 Simplifying y = 6.302775638Subproblem 2
y + -4.5 = -1.802775638 Simplifying y + -4.5 = -1.802775638 Reorder the terms: -4.5 + y = -1.802775638 Solving -4.5 + y = -1.802775638 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = -1.802775638 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -1.802775638 + 4.5 y = -1.802775638 + 4.5 Combine like terms: -1.802775638 + 4.5 = 2.697224362 y = 2.697224362 Simplifying y = 2.697224362Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.302775638, 2.697224362}
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