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Simplifying y2 + 1y = 36 Reorder the terms: 1y + y2 = 36 Solving 1y + y2 = 36 Solving for variable 'y'. Reorder the terms: -36 + 1y + y2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 1y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 1y + 36 + y2 = 0 + 36 Reorder the terms: -36 + 36 + 1y + y2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 1y + y2 = 0 + 36 1y + y2 = 0 + 36 Combine like terms: 0 + 36 = 36 1y + y2 = 36 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 = 36 + 0.25 Reorder the terms: 0.25 + y + y2 = 36 + 0.25 Combine like terms: 36 + 0.25 = 36.25 0.25 + y + y2 = 36.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (y + 0.5) equal to 6.020797289 and -6.020797289.Subproblem 1
y + 0.5 = 6.020797289 Simplifying y + 0.5 = 6.020797289 Reorder the terms: 0.5 + y = 6.020797289 Solving 0.5 + y = 6.020797289 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 = 6.020797289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 6.020797289 + -0.5 y = 6.020797289 + -0.5 Combine like terms: 6.020797289 + -0.5 = 5.520797289 y = 5.520797289 Simplifying y = 5.520797289Subproblem 2
y + 0.5 = -6.020797289 Simplifying y + 0.5 = -6.020797289 Reorder the terms: 0.5 + y = -6.020797289 Solving 0.5 + y = -6.020797289 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 = -6.020797289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -6.020797289 + -0.5 y = -6.020797289 + -0.5 Combine like terms: -6.020797289 + -0.5 = -6.520797289 y = -6.520797289 Simplifying y = -6.520797289Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.520797289, -6.520797289}
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