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Simplifying 6y2 + -45y = 8 Reorder the terms: -45y + 6y2 = 8 Solving -45y + 6y2 = 8 Solving for variable 'y'. Reorder the terms: -8 + -45y + 6y2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -45y + 6y2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.333333333 + -7.5y + y2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -7.5y + 1.333333333 + y2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -7.5y + y2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -7.5y + y2 = 0 + 1.333333333 -7.5y + y2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -7.5y + y2 = 1.333333333 The y term is -7.5y. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5y + 14.0625 + y2 = 1.333333333 + 14.0625 Reorder the terms: 14.0625 + -7.5y + y2 = 1.333333333 + 14.0625 Combine like terms: 1.333333333 + 14.0625 = 15.395833333 14.0625 + -7.5y + y2 = 15.395833333 Factor a perfect square on the left side: (y + -3.75)(y + -3.75) = 15.395833333 Calculate the square root of the right side: 3.923752456 Break this problem into two subproblems by setting (y + -3.75) equal to 3.923752456 and -3.923752456.Subproblem 1
y + -3.75 = 3.923752456 Simplifying y + -3.75 = 3.923752456 Reorder the terms: -3.75 + y = 3.923752456 Solving -3.75 + y = 3.923752456 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + y = 3.923752456 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + y = 3.923752456 + 3.75 y = 3.923752456 + 3.75 Combine like terms: 3.923752456 + 3.75 = 7.673752456 y = 7.673752456 Simplifying y = 7.673752456Subproblem 2
y + -3.75 = -3.923752456 Simplifying y + -3.75 = -3.923752456 Reorder the terms: -3.75 + y = -3.923752456 Solving -3.75 + y = -3.923752456 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + y = -3.923752456 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + y = -3.923752456 + 3.75 y = -3.923752456 + 3.75 Combine like terms: -3.923752456 + 3.75 = -0.173752456 y = -0.173752456 Simplifying y = -0.173752456Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.673752456, -0.173752456}
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