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Simplifying 9y + 3y2 = 4 Solving 9y + 3y2 = 4 Solving for variable 'y'. Reorder the terms: -4 + 9y + 3y2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 9y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + 3y + y2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 3y + 1.333333333 + y2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 3y + y2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 3y + y2 = 0 + 1.333333333 3y + y2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 3y + y2 = 1.333333333 The y term is 3y. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3y + 2.25 + y2 = 1.333333333 + 2.25 Reorder the terms: 2.25 + 3y + y2 = 1.333333333 + 2.25 Combine like terms: 1.333333333 + 2.25 = 3.583333333 2.25 + 3y + y2 = 3.583333333 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 3.583333333 Calculate the square root of the right side: 1.892969449 Break this problem into two subproblems by setting (y + 1.5) equal to 1.892969449 and -1.892969449.Subproblem 1
y + 1.5 = 1.892969449 Simplifying y + 1.5 = 1.892969449 Reorder the terms: 1.5 + y = 1.892969449 Solving 1.5 + y = 1.892969449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 1.892969449 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 1.892969449 + -1.5 y = 1.892969449 + -1.5 Combine like terms: 1.892969449 + -1.5 = 0.392969449 y = 0.392969449 Simplifying y = 0.392969449Subproblem 2
y + 1.5 = -1.892969449 Simplifying y + 1.5 = -1.892969449 Reorder the terms: 1.5 + y = -1.892969449 Solving 1.5 + y = -1.892969449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = -1.892969449 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -1.892969449 + -1.5 y = -1.892969449 + -1.5 Combine like terms: -1.892969449 + -1.5 = -3.392969449 y = -3.392969449 Simplifying y = -3.392969449Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.392969449, -3.392969449}
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