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Simplifying 4y2 + 54y + -9 = 0 Reorder the terms: -9 + 54y + 4y2 = 0 Solving -9 + 54y + 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 + 13.5y + y2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 13.5y + 2.25 + y2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 13.5y + y2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 13.5y + y2 = 0 + 2.25 13.5y + y2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 13.5y + y2 = 2.25 The y term is 13.5y. Take half its coefficient (6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. 13.5y + 45.5625 + y2 = 2.25 + 45.5625 Reorder the terms: 45.5625 + 13.5y + y2 = 2.25 + 45.5625 Combine like terms: 2.25 + 45.5625 = 47.8125 45.5625 + 13.5y + y2 = 47.8125 Factor a perfect square on the left side: (y + 6.75)(y + 6.75) = 47.8125 Calculate the square root of the right side: 6.914658343 Break this problem into two subproblems by setting (y + 6.75) equal to 6.914658343 and -6.914658343.Subproblem 1
y + 6.75 = 6.914658343 Simplifying y + 6.75 = 6.914658343 Reorder the terms: 6.75 + y = 6.914658343 Solving 6.75 + y = 6.914658343 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + y = 6.914658343 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + y = 6.914658343 + -6.75 y = 6.914658343 + -6.75 Combine like terms: 6.914658343 + -6.75 = 0.164658343 y = 0.164658343 Simplifying y = 0.164658343Subproblem 2
y + 6.75 = -6.914658343 Simplifying y + 6.75 = -6.914658343 Reorder the terms: 6.75 + y = -6.914658343 Solving 6.75 + y = -6.914658343 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + y = -6.914658343 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + y = -6.914658343 + -6.75 y = -6.914658343 + -6.75 Combine like terms: -6.914658343 + -6.75 = -13.664658343 y = -13.664658343 Simplifying y = -13.664658343Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.164658343, -13.664658343}
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