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Simplifying -1y2 + 9y + -5 = 0 Reorder the terms: -5 + 9y + -1y2 = 0 Solving -5 + 9y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -9y + y2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -9y + -5 + y2 = 0 + -5 Reorder the terms: 5 + -5 + -9y + y2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9y + y2 = 0 + -5 -9y + y2 = 0 + -5 Combine like terms: 0 + -5 = -5 -9y + y2 = -5 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 = -5 + 20.25 Reorder the terms: 20.25 + -9y + y2 = -5 + 20.25 Combine like terms: -5 + 20.25 = 15.25 20.25 + -9y + y2 = 15.25 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (y + -4.5) equal to 3.905124838 and -3.905124838.Subproblem 1
y + -4.5 = 3.905124838 Simplifying y + -4.5 = 3.905124838 Reorder the terms: -4.5 + y = 3.905124838 Solving -4.5 + y = 3.905124838 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 = 3.905124838 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 3.905124838 + 4.5 y = 3.905124838 + 4.5 Combine like terms: 3.905124838 + 4.5 = 8.405124838 y = 8.405124838 Simplifying y = 8.405124838Subproblem 2
y + -4.5 = -3.905124838 Simplifying y + -4.5 = -3.905124838 Reorder the terms: -4.5 + y = -3.905124838 Solving -4.5 + y = -3.905124838 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 = -3.905124838 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -3.905124838 + 4.5 y = -3.905124838 + 4.5 Combine like terms: -3.905124838 + 4.5 = 0.594875162 y = 0.594875162 Simplifying y = 0.594875162Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.405124838, 0.594875162}
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