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Simplifying 0 = y2 + -21y + 66 Reorder the terms: 0 = 66 + -21y + y2 Solving 0 = 66 + -21y + y2 Solving for variable 'y'. Combine like terms: 0 + -66 = -66 -66 + 21y + -1y2 = 66 + -21y + y2 + -66 + 21y + -1y2 Reorder the terms: -66 + 21y + -1y2 = 66 + -66 + -21y + 21y + y2 + -1y2 Combine like terms: 66 + -66 = 0 -66 + 21y + -1y2 = 0 + -21y + 21y + y2 + -1y2 -66 + 21y + -1y2 = -21y + 21y + y2 + -1y2 Combine like terms: -21y + 21y = 0 -66 + 21y + -1y2 = 0 + y2 + -1y2 -66 + 21y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -66 + 21y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 66 + -21y + y2 = 0 Move the constant term to the right: Add '-66' to each side of the equation. 66 + -21y + -66 + y2 = 0 + -66 Reorder the terms: 66 + -66 + -21y + y2 = 0 + -66 Combine like terms: 66 + -66 = 0 0 + -21y + y2 = 0 + -66 -21y + y2 = 0 + -66 Combine like terms: 0 + -66 = -66 -21y + y2 = -66 The y term is -21y. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21y + 110.25 + y2 = -66 + 110.25 Reorder the terms: 110.25 + -21y + y2 = -66 + 110.25 Combine like terms: -66 + 110.25 = 44.25 110.25 + -21y + y2 = 44.25 Factor a perfect square on the left side: (y + -10.5)(y + -10.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (y + -10.5) equal to 6.652067348 and -6.652067348.Subproblem 1
y + -10.5 = 6.652067348 Simplifying y + -10.5 = 6.652067348 Reorder the terms: -10.5 + y = 6.652067348 Solving -10.5 + y = 6.652067348 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + y = 6.652067348 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + y = 6.652067348 + 10.5 y = 6.652067348 + 10.5 Combine like terms: 6.652067348 + 10.5 = 17.152067348 y = 17.152067348 Simplifying y = 17.152067348Subproblem 2
y + -10.5 = -6.652067348 Simplifying y + -10.5 = -6.652067348 Reorder the terms: -10.5 + y = -6.652067348 Solving -10.5 + y = -6.652067348 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + y = -6.652067348 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + y = -6.652067348 + 10.5 y = -6.652067348 + 10.5 Combine like terms: -6.652067348 + 10.5 = 3.847932652 y = 3.847932652 Simplifying y = 3.847932652Solution
The solution to the problem is based on the solutions from the subproblems. y = {17.152067348, 3.847932652}
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