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Simplifying 9y2 + 36y + -124 = 0 Reorder the terms: -124 + 36y + 9y2 = 0 Solving -124 + 36y + 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'. -13.77777778 + 4y + y2 = 0 Move the constant term to the right: Add '13.77777778' to each side of the equation. -13.77777778 + 4y + 13.77777778 + y2 = 0 + 13.77777778 Reorder the terms: -13.77777778 + 13.77777778 + 4y + y2 = 0 + 13.77777778 Combine like terms: -13.77777778 + 13.77777778 = 0.00000000 0.00000000 + 4y + y2 = 0 + 13.77777778 4y + y2 = 0 + 13.77777778 Combine like terms: 0 + 13.77777778 = 13.77777778 4y + y2 = 13.77777778 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 13.77777778 + 4 Reorder the terms: 4 + 4y + y2 = 13.77777778 + 4 Combine like terms: 13.77777778 + 4 = 17.77777778 4 + 4y + y2 = 17.77777778 Factor a perfect square on the left side: (y + 2)(y + 2) = 17.77777778 Calculate the square root of the right side: 4.216370214 Break this problem into two subproblems by setting (y + 2) equal to 4.216370214 and -4.216370214.Subproblem 1
y + 2 = 4.216370214 Simplifying y + 2 = 4.216370214 Reorder the terms: 2 + y = 4.216370214 Solving 2 + y = 4.216370214 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 4.216370214 + -2 Combine like terms: 2 + -2 = 0 0 + y = 4.216370214 + -2 y = 4.216370214 + -2 Combine like terms: 4.216370214 + -2 = 2.216370214 y = 2.216370214 Simplifying y = 2.216370214Subproblem 2
y + 2 = -4.216370214 Simplifying y + 2 = -4.216370214 Reorder the terms: 2 + y = -4.216370214 Solving 2 + y = -4.216370214 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -4.216370214 + -2 Combine like terms: 2 + -2 = 0 0 + y = -4.216370214 + -2 y = -4.216370214 + -2 Combine like terms: -4.216370214 + -2 = -6.216370214 y = -6.216370214 Simplifying y = -6.216370214Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.216370214, -6.216370214}
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