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Simplifying y2 + 32y + -384 = 0 Reorder the terms: -384 + 32y + y2 = 0 Solving -384 + 32y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '384' to each side of the equation. -384 + 32y + 384 + y2 = 0 + 384 Reorder the terms: -384 + 384 + 32y + y2 = 0 + 384 Combine like terms: -384 + 384 = 0 0 + 32y + y2 = 0 + 384 32y + y2 = 0 + 384 Combine like terms: 0 + 384 = 384 32y + y2 = 384 The y term is 32y. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32y + 256 + y2 = 384 + 256 Reorder the terms: 256 + 32y + y2 = 384 + 256 Combine like terms: 384 + 256 = 640 256 + 32y + y2 = 640 Factor a perfect square on the left side: (y + 16)(y + 16) = 640 Calculate the square root of the right side: 25.298221281 Break this problem into two subproblems by setting (y + 16) equal to 25.298221281 and -25.298221281.Subproblem 1
y + 16 = 25.298221281 Simplifying y + 16 = 25.298221281 Reorder the terms: 16 + y = 25.298221281 Solving 16 + y = 25.298221281 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + y = 25.298221281 + -16 Combine like terms: 16 + -16 = 0 0 + y = 25.298221281 + -16 y = 25.298221281 + -16 Combine like terms: 25.298221281 + -16 = 9.298221281 y = 9.298221281 Simplifying y = 9.298221281Subproblem 2
y + 16 = -25.298221281 Simplifying y + 16 = -25.298221281 Reorder the terms: 16 + y = -25.298221281 Solving 16 + y = -25.298221281 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + y = -25.298221281 + -16 Combine like terms: 16 + -16 = 0 0 + y = -25.298221281 + -16 y = -25.298221281 + -16 Combine like terms: -25.298221281 + -16 = -41.298221281 y = -41.298221281 Simplifying y = -41.298221281Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.298221281, -41.298221281}
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