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Simplifying (5y2) + -28y + -48 = 0 Reorder the terms: -48 + -28y + (5y2) = 0 Solving -48 + -28y + (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 + -5.6y + y2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + -5.6y + 9.6 + y2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + -5.6y + y2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + -5.6y + y2 = 0 + 9.6 -5.6y + y2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 -5.6y + y2 = 9.6 The y term is -5.6y. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6y + 7.84 + y2 = 9.6 + 7.84 Reorder the terms: 7.84 + -5.6y + y2 = 9.6 + 7.84 Combine like terms: 9.6 + 7.84 = 17.44 7.84 + -5.6y + y2 = 17.44 Factor a perfect square on the left side: ((y) + -2.8)((y) + -2.8) = 17.44 Calculate the square root of the right side: 4.176122604 Break this problem into two subproblems by setting ((y) + -2.8) equal to 4.176122604 and -4.176122604.Subproblem 1
(y) + -2.8 = 4.176122604 Simplifying (y) + -2.8 = 4.176122604 y + -2.8 = 4.176122604 Reorder the terms: -2.8 + y = 4.176122604 Solving -2.8 + y = 4.176122604 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + y = 4.176122604 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + y = 4.176122604 + 2.8 y = 4.176122604 + 2.8 Combine like terms: 4.176122604 + 2.8 = 6.976122604 y = 6.976122604 Simplifying y = 6.976122604Subproblem 2
(y) + -2.8 = -4.176122604 Simplifying (y) + -2.8 = -4.176122604 y + -2.8 = -4.176122604 Reorder the terms: -2.8 + y = -4.176122604 Solving -2.8 + y = -4.176122604 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + y = -4.176122604 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + y = -4.176122604 + 2.8 y = -4.176122604 + 2.8 Combine like terms: -4.176122604 + 2.8 = -1.376122604 y = -1.376122604 Simplifying y = -1.376122604Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.976122604, -1.376122604}
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