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Simplifying 3y2 + -9y = 125 Reorder the terms: -9y + 3y2 = 125 Solving -9y + 3y2 = 125 Solving for variable 'y'. Reorder the terms: -125 + -9y + 3y2 = 125 + -125 Combine like terms: 125 + -125 = 0 -125 + -9y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -41.66666667 + -3y + y2 = 0 Move the constant term to the right: Add '41.66666667' to each side of the equation. -41.66666667 + -3y + 41.66666667 + y2 = 0 + 41.66666667 Reorder the terms: -41.66666667 + 41.66666667 + -3y + y2 = 0 + 41.66666667 Combine like terms: -41.66666667 + 41.66666667 = 0.00000000 0.00000000 + -3y + y2 = 0 + 41.66666667 -3y + y2 = 0 + 41.66666667 Combine like terms: 0 + 41.66666667 = 41.66666667 -3y + y2 = 41.66666667 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 41.66666667 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 41.66666667 + 2.25 Combine like terms: 41.66666667 + 2.25 = 43.91666667 2.25 + -3y + y2 = 43.91666667 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 43.91666667 Calculate the square root of the right side: 6.626965118 Break this problem into two subproblems by setting (y + -1.5) equal to 6.626965118 and -6.626965118.Subproblem 1
y + -1.5 = 6.626965118 Simplifying y + -1.5 = 6.626965118 Reorder the terms: -1.5 + y = 6.626965118 Solving -1.5 + y = 6.626965118 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 6.626965118 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 6.626965118 + 1.5 y = 6.626965118 + 1.5 Combine like terms: 6.626965118 + 1.5 = 8.126965118 y = 8.126965118 Simplifying y = 8.126965118Subproblem 2
y + -1.5 = -6.626965118 Simplifying y + -1.5 = -6.626965118 Reorder the terms: -1.5 + y = -6.626965118 Solving -1.5 + y = -6.626965118 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -6.626965118 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -6.626965118 + 1.5 y = -6.626965118 + 1.5 Combine like terms: -6.626965118 + 1.5 = -5.126965118 y = -5.126965118 Simplifying y = -5.126965118Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.126965118, -5.126965118}
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