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Simplifying 4y2 + 24y + 9 = 0 Reorder the terms: 9 + 24y + 4y2 = 0 Solving 9 + 24y + 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'. 2.25 + 6y + y2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 6y + -2.25 + y2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 6y + y2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 6y + y2 = 0 + -2.25 6y + y2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 6y + y2 = -2.25 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = -2.25 + 9 Reorder the terms: 9 + 6y + y2 = -2.25 + 9 Combine like terms: -2.25 + 9 = 6.75 9 + 6y + y2 = 6.75 Factor a perfect square on the left side: (y + 3)(y + 3) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (y + 3) equal to 2.598076211 and -2.598076211.Subproblem 1
y + 3 = 2.598076211 Simplifying y + 3 = 2.598076211 Reorder the terms: 3 + y = 2.598076211 Solving 3 + y = 2.598076211 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 2.598076211 + -3 Combine like terms: 3 + -3 = 0 0 + y = 2.598076211 + -3 y = 2.598076211 + -3 Combine like terms: 2.598076211 + -3 = -0.401923789 y = -0.401923789 Simplifying y = -0.401923789Subproblem 2
y + 3 = -2.598076211 Simplifying y + 3 = -2.598076211 Reorder the terms: 3 + y = -2.598076211 Solving 3 + y = -2.598076211 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -2.598076211 + -3 Combine like terms: 3 + -3 = 0 0 + y = -2.598076211 + -3 y = -2.598076211 + -3 Combine like terms: -2.598076211 + -3 = -5.598076211 y = -5.598076211 Simplifying y = -5.598076211Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.401923789, -5.598076211}
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