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Simplifying y2 + 13y = 56 Reorder the terms: 13y + y2 = 56 Solving 13y + y2 = 56 Solving for variable 'y'. Reorder the terms: -56 + 13y + y2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + 13y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 13y + 56 + y2 = 0 + 56 Reorder the terms: -56 + 56 + 13y + y2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 13y + y2 = 0 + 56 13y + y2 = 0 + 56 Combine like terms: 0 + 56 = 56 13y + y2 = 56 The y term is 13y. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13y + 42.25 + y2 = 56 + 42.25 Reorder the terms: 42.25 + 13y + y2 = 56 + 42.25 Combine like terms: 56 + 42.25 = 98.25 42.25 + 13y + y2 = 98.25 Factor a perfect square on the left side: (y + 6.5)(y + 6.5) = 98.25 Calculate the square root of the right side: 9.912113801 Break this problem into two subproblems by setting (y + 6.5) equal to 9.912113801 and -9.912113801.Subproblem 1
y + 6.5 = 9.912113801 Simplifying y + 6.5 = 9.912113801 Reorder the terms: 6.5 + y = 9.912113801 Solving 6.5 + y = 9.912113801 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + y = 9.912113801 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + y = 9.912113801 + -6.5 y = 9.912113801 + -6.5 Combine like terms: 9.912113801 + -6.5 = 3.412113801 y = 3.412113801 Simplifying y = 3.412113801Subproblem 2
y + 6.5 = -9.912113801 Simplifying y + 6.5 = -9.912113801 Reorder the terms: 6.5 + y = -9.912113801 Solving 6.5 + y = -9.912113801 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + y = -9.912113801 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + y = -9.912113801 + -6.5 y = -9.912113801 + -6.5 Combine like terms: -9.912113801 + -6.5 = -16.412113801 y = -16.412113801 Simplifying y = -16.412113801Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.412113801, -16.412113801}
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