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Simplifying 4y2 + -5y + -30 = 0 Reorder the terms: -30 + -5y + 4y2 = 0 Solving -30 + -5y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.5 + -1.25y + y2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -1.25y + 7.5 + y2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -1.25y + y2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -1.25y + y2 = 0 + 7.5 -1.25y + y2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -1.25y + y2 = 7.5 The y term is -1.25y. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25y + 0.390625 + y2 = 7.5 + 0.390625 Reorder the terms: 0.390625 + -1.25y + y2 = 7.5 + 0.390625 Combine like terms: 7.5 + 0.390625 = 7.890625 0.390625 + -1.25y + y2 = 7.890625 Factor a perfect square on the left side: (y + -0.625)(y + -0.625) = 7.890625 Calculate the square root of the right side: 2.809025632 Break this problem into two subproblems by setting (y + -0.625) equal to 2.809025632 and -2.809025632.Subproblem 1
y + -0.625 = 2.809025632 Simplifying y + -0.625 = 2.809025632 Reorder the terms: -0.625 + y = 2.809025632 Solving -0.625 + y = 2.809025632 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + y = 2.809025632 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + y = 2.809025632 + 0.625 y = 2.809025632 + 0.625 Combine like terms: 2.809025632 + 0.625 = 3.434025632 y = 3.434025632 Simplifying y = 3.434025632Subproblem 2
y + -0.625 = -2.809025632 Simplifying y + -0.625 = -2.809025632 Reorder the terms: -0.625 + y = -2.809025632 Solving -0.625 + y = -2.809025632 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + y = -2.809025632 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + y = -2.809025632 + 0.625 y = -2.809025632 + 0.625 Combine like terms: -2.809025632 + 0.625 = -2.184025632 y = -2.184025632 Simplifying y = -2.184025632Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.434025632, -2.184025632}
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