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Simplifying 2y2 + 7y + -81 = 0 Reorder the terms: -81 + 7y + 2y2 = 0 Solving -81 + 7y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -40.5 + 3.5y + y2 = 0 Move the constant term to the right: Add '40.5' to each side of the equation. -40.5 + 3.5y + 40.5 + y2 = 0 + 40.5 Reorder the terms: -40.5 + 40.5 + 3.5y + y2 = 0 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + 3.5y + y2 = 0 + 40.5 3.5y + y2 = 0 + 40.5 Combine like terms: 0 + 40.5 = 40.5 3.5y + y2 = 40.5 The y term is 3.5y. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5y + 3.0625 + y2 = 40.5 + 3.0625 Reorder the terms: 3.0625 + 3.5y + y2 = 40.5 + 3.0625 Combine like terms: 40.5 + 3.0625 = 43.5625 3.0625 + 3.5y + y2 = 43.5625 Factor a perfect square on the left side: (y + 1.75)(y + 1.75) = 43.5625 Calculate the square root of the right side: 6.600189391 Break this problem into two subproblems by setting (y + 1.75) equal to 6.600189391 and -6.600189391.Subproblem 1
y + 1.75 = 6.600189391 Simplifying y + 1.75 = 6.600189391 Reorder the terms: 1.75 + y = 6.600189391 Solving 1.75 + y = 6.600189391 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = 6.600189391 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = 6.600189391 + -1.75 y = 6.600189391 + -1.75 Combine like terms: 6.600189391 + -1.75 = 4.850189391 y = 4.850189391 Simplifying y = 4.850189391Subproblem 2
y + 1.75 = -6.600189391 Simplifying y + 1.75 = -6.600189391 Reorder the terms: 1.75 + y = -6.600189391 Solving 1.75 + y = -6.600189391 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = -6.600189391 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = -6.600189391 + -1.75 y = -6.600189391 + -1.75 Combine like terms: -6.600189391 + -1.75 = -8.350189391 y = -8.350189391 Simplifying y = -8.350189391Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.850189391, -8.350189391}
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