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Simplifying 96 + 18y + 5y2 = 192 Solving 96 + 18y + 5y2 = 192 Solving for variable 'y'. Reorder the terms: 96 + -192 + 18y + 5y2 = 192 + -192 Combine like terms: 96 + -192 = -96 -96 + 18y + 5y2 = 192 + -192 Combine like terms: 192 + -192 = 0 -96 + 18y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -19.2 + 3.6y + y2 = 0 Move the constant term to the right: Add '19.2' to each side of the equation. -19.2 + 3.6y + 19.2 + y2 = 0 + 19.2 Reorder the terms: -19.2 + 19.2 + 3.6y + y2 = 0 + 19.2 Combine like terms: -19.2 + 19.2 = 0.0 0.0 + 3.6y + y2 = 0 + 19.2 3.6y + y2 = 0 + 19.2 Combine like terms: 0 + 19.2 = 19.2 3.6y + y2 = 19.2 The y term is 3.6y. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6y + 3.24 + y2 = 19.2 + 3.24 Reorder the terms: 3.24 + 3.6y + y2 = 19.2 + 3.24 Combine like terms: 19.2 + 3.24 = 22.44 3.24 + 3.6y + y2 = 22.44 Factor a perfect square on the left side: (y + 1.8)(y + 1.8) = 22.44 Calculate the square root of the right side: 4.737087713 Break this problem into two subproblems by setting (y + 1.8) equal to 4.737087713 and -4.737087713.Subproblem 1
y + 1.8 = 4.737087713 Simplifying y + 1.8 = 4.737087713 Reorder the terms: 1.8 + y = 4.737087713 Solving 1.8 + y = 4.737087713 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + y = 4.737087713 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + y = 4.737087713 + -1.8 y = 4.737087713 + -1.8 Combine like terms: 4.737087713 + -1.8 = 2.937087713 y = 2.937087713 Simplifying y = 2.937087713Subproblem 2
y + 1.8 = -4.737087713 Simplifying y + 1.8 = -4.737087713 Reorder the terms: 1.8 + y = -4.737087713 Solving 1.8 + y = -4.737087713 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + y = -4.737087713 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + y = -4.737087713 + -1.8 y = -4.737087713 + -1.8 Combine like terms: -4.737087713 + -1.8 = -6.537087713 y = -6.537087713 Simplifying y = -6.537087713Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.937087713, -6.537087713}
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