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Simplifying 6y2 + -15y + -11 = 0 Reorder the terms: -11 + -15y + 6y2 = 0 Solving -11 + -15y + 6y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.833333333 + -2.5y + y2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + -2.5y + 1.833333333 + y2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + -2.5y + y2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + -2.5y + y2 = 0 + 1.833333333 -2.5y + y2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 -2.5y + y2 = 1.833333333 The y term is -2.5y. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5y + 1.5625 + y2 = 1.833333333 + 1.5625 Reorder the terms: 1.5625 + -2.5y + y2 = 1.833333333 + 1.5625 Combine like terms: 1.833333333 + 1.5625 = 3.395833333 1.5625 + -2.5y + y2 = 3.395833333 Factor a perfect square on the left side: (y + -1.25)(y + -1.25) = 3.395833333 Calculate the square root of the right side: 1.842778699 Break this problem into two subproblems by setting (y + -1.25) equal to 1.842778699 and -1.842778699.Subproblem 1
y + -1.25 = 1.842778699 Simplifying y + -1.25 = 1.842778699 Reorder the terms: -1.25 + y = 1.842778699 Solving -1.25 + y = 1.842778699 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + y = 1.842778699 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = 1.842778699 + 1.25 y = 1.842778699 + 1.25 Combine like terms: 1.842778699 + 1.25 = 3.092778699 y = 3.092778699 Simplifying y = 3.092778699Subproblem 2
y + -1.25 = -1.842778699 Simplifying y + -1.25 = -1.842778699 Reorder the terms: -1.25 + y = -1.842778699 Solving -1.25 + y = -1.842778699 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + y = -1.842778699 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = -1.842778699 + 1.25 y = -1.842778699 + 1.25 Combine like terms: -1.842778699 + 1.25 = -0.592778699 y = -0.592778699 Simplifying y = -0.592778699Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.092778699, -0.592778699}
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