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Simplifying 4y2 + 9y + -6 = 0 Reorder the terms: -6 + 9y + 4y2 = 0 Solving -6 + 9y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + 2.25y + y2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 2.25y + 1.5 + y2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 2.25y + y2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 2.25y + y2 = 0 + 1.5 2.25y + y2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 2.25y + y2 = 1.5 The y term is 2.25y. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25y + 1.265625 + y2 = 1.5 + 1.265625 Reorder the terms: 1.265625 + 2.25y + y2 = 1.5 + 1.265625 Combine like terms: 1.5 + 1.265625 = 2.765625 1.265625 + 2.25y + y2 = 2.765625 Factor a perfect square on the left side: (y + 1.125)(y + 1.125) = 2.765625 Calculate the square root of the right side: 1.663016837 Break this problem into two subproblems by setting (y + 1.125) equal to 1.663016837 and -1.663016837.Subproblem 1
y + 1.125 = 1.663016837 Simplifying y + 1.125 = 1.663016837 Reorder the terms: 1.125 + y = 1.663016837 Solving 1.125 + y = 1.663016837 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + y = 1.663016837 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + y = 1.663016837 + -1.125 y = 1.663016837 + -1.125 Combine like terms: 1.663016837 + -1.125 = 0.538016837 y = 0.538016837 Simplifying y = 0.538016837Subproblem 2
y + 1.125 = -1.663016837 Simplifying y + 1.125 = -1.663016837 Reorder the terms: 1.125 + y = -1.663016837 Solving 1.125 + y = -1.663016837 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + y = -1.663016837 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + y = -1.663016837 + -1.125 y = -1.663016837 + -1.125 Combine like terms: -1.663016837 + -1.125 = -2.788016837 y = -2.788016837 Simplifying y = -2.788016837Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.538016837, -2.788016837}
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