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Simplifying 9y2 + 37y + 9 = 0 Reorder the terms: 9 + 37y + 9y2 = 0 Solving 9 + 37y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1 + 4.111111111y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4.111111111y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + 4.111111111y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4.111111111y + y2 = 0 + -1 4.111111111y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 4.111111111y + y2 = -1 The y term is 4.111111111y. Take half its coefficient (2.055555556). Square it (4.225308644) and add it to both sides. Add '4.225308644' to each side of the equation. 4.111111111y + 4.225308644 + y2 = -1 + 4.225308644 Reorder the terms: 4.225308644 + 4.111111111y + y2 = -1 + 4.225308644 Combine like terms: -1 + 4.225308644 = 3.225308644 4.225308644 + 4.111111111y + y2 = 3.225308644 Factor a perfect square on the left side: (y + 2.055555556)(y + 2.055555556) = 3.225308644 Calculate the square root of the right side: 1.795914431 Break this problem into two subproblems by setting (y + 2.055555556) equal to 1.795914431 and -1.795914431.Subproblem 1
y + 2.055555556 = 1.795914431 Simplifying y + 2.055555556 = 1.795914431 Reorder the terms: 2.055555556 + y = 1.795914431 Solving 2.055555556 + y = 1.795914431 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.055555556' to each side of the equation. 2.055555556 + -2.055555556 + y = 1.795914431 + -2.055555556 Combine like terms: 2.055555556 + -2.055555556 = 0.000000000 0.000000000 + y = 1.795914431 + -2.055555556 y = 1.795914431 + -2.055555556 Combine like terms: 1.795914431 + -2.055555556 = -0.259641125 y = -0.259641125 Simplifying y = -0.259641125Subproblem 2
y + 2.055555556 = -1.795914431 Simplifying y + 2.055555556 = -1.795914431 Reorder the terms: 2.055555556 + y = -1.795914431 Solving 2.055555556 + y = -1.795914431 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.055555556' to each side of the equation. 2.055555556 + -2.055555556 + y = -1.795914431 + -2.055555556 Combine like terms: 2.055555556 + -2.055555556 = 0.000000000 0.000000000 + y = -1.795914431 + -2.055555556 y = -1.795914431 + -2.055555556 Combine like terms: -1.795914431 + -2.055555556 = -3.851469987 y = -3.851469987 Simplifying y = -3.851469987Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.259641125, -3.851469987}
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