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Simplifying 5y2 + -48y + -720 = 0 Reorder the terms: -720 + -48y + 5y2 = 0 Solving -720 + -48y + 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'. -144 + -9.6y + y2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + -9.6y + 144 + y2 = 0 + 144 Reorder the terms: -144 + 144 + -9.6y + y2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -9.6y + y2 = 0 + 144 -9.6y + y2 = 0 + 144 Combine like terms: 0 + 144 = 144 -9.6y + y2 = 144 The y term is -9.6y. Take half its coefficient (-4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. -9.6y + 23.04 + y2 = 144 + 23.04 Reorder the terms: 23.04 + -9.6y + y2 = 144 + 23.04 Combine like terms: 144 + 23.04 = 167.04 23.04 + -9.6y + y2 = 167.04 Factor a perfect square on the left side: (y + -4.8)(y + -4.8) = 167.04 Calculate the square root of the right side: 12.924395537 Break this problem into two subproblems by setting (y + -4.8) equal to 12.924395537 and -12.924395537.Subproblem 1
y + -4.8 = 12.924395537 Simplifying y + -4.8 = 12.924395537 Reorder the terms: -4.8 + y = 12.924395537 Solving -4.8 + y = 12.924395537 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + y = 12.924395537 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + y = 12.924395537 + 4.8 y = 12.924395537 + 4.8 Combine like terms: 12.924395537 + 4.8 = 17.724395537 y = 17.724395537 Simplifying y = 17.724395537Subproblem 2
y + -4.8 = -12.924395537 Simplifying y + -4.8 = -12.924395537 Reorder the terms: -4.8 + y = -12.924395537 Solving -4.8 + y = -12.924395537 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + y = -12.924395537 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + y = -12.924395537 + 4.8 y = -12.924395537 + 4.8 Combine like terms: -12.924395537 + 4.8 = -8.124395537 y = -8.124395537 Simplifying y = -8.124395537Solution
The solution to the problem is based on the solutions from the subproblems. y = {17.724395537, -8.124395537}
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