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Simplifying y2 + 16y + -240 = 0 Reorder the terms: -240 + 16y + y2 = 0 Solving -240 + 16y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 16y + 240 + y2 = 0 + 240 Reorder the terms: -240 + 240 + 16y + y2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 16y + y2 = 0 + 240 16y + y2 = 0 + 240 Combine like terms: 0 + 240 = 240 16y + y2 = 240 The y term is 16y. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16y + 64 + y2 = 240 + 64 Reorder the terms: 64 + 16y + y2 = 240 + 64 Combine like terms: 240 + 64 = 304 64 + 16y + y2 = 304 Factor a perfect square on the left side: (y + 8)(y + 8) = 304 Calculate the square root of the right side: 17.435595774 Break this problem into two subproblems by setting (y + 8) equal to 17.435595774 and -17.435595774.Subproblem 1
y + 8 = 17.435595774 Simplifying y + 8 = 17.435595774 Reorder the terms: 8 + y = 17.435595774 Solving 8 + y = 17.435595774 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = 17.435595774 + -8 Combine like terms: 8 + -8 = 0 0 + y = 17.435595774 + -8 y = 17.435595774 + -8 Combine like terms: 17.435595774 + -8 = 9.435595774 y = 9.435595774 Simplifying y = 9.435595774Subproblem 2
y + 8 = -17.435595774 Simplifying y + 8 = -17.435595774 Reorder the terms: 8 + y = -17.435595774 Solving 8 + y = -17.435595774 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = -17.435595774 + -8 Combine like terms: 8 + -8 = 0 0 + y = -17.435595774 + -8 y = -17.435595774 + -8 Combine like terms: -17.435595774 + -8 = -25.435595774 y = -25.435595774 Simplifying y = -25.435595774Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.435595774, -25.435595774}
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