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Simplifying -6y2 + -9y = -11 Reorder the terms: -9y + -6y2 = -11 Solving -9y + -6y2 = -11 Solving for variable 'y'. Reorder the terms: 11 + -9y + -6y2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + -9y + -6y2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.833333333 + 1.5y + y2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + 1.5y + 1.833333333 + y2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + 1.5y + y2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + 1.5y + y2 = 0 + 1.833333333 1.5y + y2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 1.5y + y2 = 1.833333333 The y term is 1.5y. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5y + 0.5625 + y2 = 1.833333333 + 0.5625 Reorder the terms: 0.5625 + 1.5y + y2 = 1.833333333 + 0.5625 Combine like terms: 1.833333333 + 0.5625 = 2.395833333 0.5625 + 1.5y + y2 = 2.395833333 Factor a perfect square on the left side: (y + 0.75)(y + 0.75) = 2.395833333 Calculate the square root of the right side: 1.547847968 Break this problem into two subproblems by setting (y + 0.75) equal to 1.547847968 and -1.547847968.Subproblem 1
y + 0.75 = 1.547847968 Simplifying y + 0.75 = 1.547847968 Reorder the terms: 0.75 + y = 1.547847968 Solving 0.75 + y = 1.547847968 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y = 1.547847968 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = 1.547847968 + -0.75 y = 1.547847968 + -0.75 Combine like terms: 1.547847968 + -0.75 = 0.797847968 y = 0.797847968 Simplifying y = 0.797847968Subproblem 2
y + 0.75 = -1.547847968 Simplifying y + 0.75 = -1.547847968 Reorder the terms: 0.75 + y = -1.547847968 Solving 0.75 + y = -1.547847968 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y = -1.547847968 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = -1.547847968 + -0.75 y = -1.547847968 + -0.75 Combine like terms: -1.547847968 + -0.75 = -2.297847968 y = -2.297847968 Simplifying y = -2.297847968Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.797847968, -2.297847968}
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