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Simplifying 5y2 + -36y + -48 = 0 Reorder the terms: -48 + -36y + 5y2 = 0 Solving -48 + -36y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.6 + -7.2y + y2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + -7.2y + 9.6 + y2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + -7.2y + y2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + -7.2y + y2 = 0 + 9.6 -7.2y + y2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 -7.2y + y2 = 9.6 The y term is -7.2y. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2y + 12.96 + y2 = 9.6 + 12.96 Reorder the terms: 12.96 + -7.2y + y2 = 9.6 + 12.96 Combine like terms: 9.6 + 12.96 = 22.56 12.96 + -7.2y + y2 = 22.56 Factor a perfect square on the left side: (y + -3.6)(y + -3.6) = 22.56 Calculate the square root of the right side: 4.749736835 Break this problem into two subproblems by setting (y + -3.6) equal to 4.749736835 and -4.749736835.Subproblem 1
y + -3.6 = 4.749736835 Simplifying y + -3.6 = 4.749736835 Reorder the terms: -3.6 + y = 4.749736835 Solving -3.6 + y = 4.749736835 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + y = 4.749736835 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + y = 4.749736835 + 3.6 y = 4.749736835 + 3.6 Combine like terms: 4.749736835 + 3.6 = 8.349736835 y = 8.349736835 Simplifying y = 8.349736835Subproblem 2
y + -3.6 = -4.749736835 Simplifying y + -3.6 = -4.749736835 Reorder the terms: -3.6 + y = -4.749736835 Solving -3.6 + y = -4.749736835 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + y = -4.749736835 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + y = -4.749736835 + 3.6 y = -4.749736835 + 3.6 Combine like terms: -4.749736835 + 3.6 = -1.149736835 y = -1.149736835 Simplifying y = -1.149736835Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.349736835, -1.149736835}
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