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Simplifying 168 = 6y + 10 + y2 + 3y Reorder the terms: 168 = 10 + 6y + 3y + y2 Combine like terms: 6y + 3y = 9y 168 = 10 + 9y + y2 Solving 168 = 10 + 9y + y2 Solving for variable 'y'. Combine like terms: 168 + -10 = 158 158 + -9y + -1y2 = 10 + 9y + y2 + -10 + -9y + -1y2 Reorder the terms: 158 + -9y + -1y2 = 10 + -10 + 9y + -9y + y2 + -1y2 Combine like terms: 10 + -10 = 0 158 + -9y + -1y2 = 0 + 9y + -9y + y2 + -1y2 158 + -9y + -1y2 = 9y + -9y + y2 + -1y2 Combine like terms: 9y + -9y = 0 158 + -9y + -1y2 = 0 + y2 + -1y2 158 + -9y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 158 + -9y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -158 + 9y + y2 = 0 Move the constant term to the right: Add '158' to each side of the equation. -158 + 9y + 158 + y2 = 0 + 158 Reorder the terms: -158 + 158 + 9y + y2 = 0 + 158 Combine like terms: -158 + 158 = 0 0 + 9y + y2 = 0 + 158 9y + y2 = 0 + 158 Combine like terms: 0 + 158 = 158 9y + y2 = 158 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 = 158 + 20.25 Reorder the terms: 20.25 + 9y + y2 = 158 + 20.25 Combine like terms: 158 + 20.25 = 178.25 20.25 + 9y + y2 = 178.25 Factor a perfect square on the left side: (y + 4.5)(y + 4.5) = 178.25 Calculate the square root of the right side: 13.351029923 Break this problem into two subproblems by setting (y + 4.5) equal to 13.351029923 and -13.351029923.Subproblem 1
y + 4.5 = 13.351029923 Simplifying y + 4.5 = 13.351029923 Reorder the terms: 4.5 + y = 13.351029923 Solving 4.5 + y = 13.351029923 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 = 13.351029923 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = 13.351029923 + -4.5 y = 13.351029923 + -4.5 Combine like terms: 13.351029923 + -4.5 = 8.851029923 y = 8.851029923 Simplifying y = 8.851029923Subproblem 2
y + 4.5 = -13.351029923 Simplifying y + 4.5 = -13.351029923 Reorder the terms: 4.5 + y = -13.351029923 Solving 4.5 + y = -13.351029923 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 = -13.351029923 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = -13.351029923 + -4.5 y = -13.351029923 + -4.5 Combine like terms: -13.351029923 + -4.5 = -17.851029923 y = -17.851029923 Simplifying y = -17.851029923Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.851029923, -17.851029923}
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