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Simplifying y2 + 2y + -48 = y Reorder the terms: -48 + 2y + y2 = y Solving -48 + 2y + y2 = y Solving for variable 'y'. Reorder the terms: -48 + 2y + -1y + y2 = y + -1y Combine like terms: 2y + -1y = 1y -48 + 1y + y2 = y + -1y Combine like terms: y + -1y = 0 -48 + 1y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 1y + 48 + y2 = 0 + 48 Reorder the terms: -48 + 48 + 1y + y2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 1y + y2 = 0 + 48 1y + y2 = 0 + 48 Combine like terms: 0 + 48 = 48 1y + y2 = 48 The y term is 1y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. y + 0.25 + y2 = 48 + 0.25 Reorder the terms: 0.25 + y + y2 = 48 + 0.25 Combine like terms: 48 + 0.25 = 48.25 0.25 + y + y2 = 48.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (y + 0.5) equal to 6.946221995 and -6.946221995.Subproblem 1
y + 0.5 = 6.946221995 Simplifying y + 0.5 = 6.946221995 Reorder the terms: 0.5 + y = 6.946221995 Solving 0.5 + y = 6.946221995 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 6.946221995 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 6.946221995 + -0.5 y = 6.946221995 + -0.5 Combine like terms: 6.946221995 + -0.5 = 6.446221995 y = 6.446221995 Simplifying y = 6.446221995Subproblem 2
y + 0.5 = -6.946221995 Simplifying y + 0.5 = -6.946221995 Reorder the terms: 0.5 + y = -6.946221995 Solving 0.5 + y = -6.946221995 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -6.946221995 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -6.946221995 + -0.5 y = -6.946221995 + -0.5 Combine like terms: -6.946221995 + -0.5 = -7.446221995 y = -7.446221995 Simplifying y = -7.446221995Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.446221995, -7.446221995}
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