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Simplifying y2 + 4y = 41 Reorder the terms: 4y + y2 = 41 Solving 4y + y2 = 41 Solving for variable 'y'. Reorder the terms: -41 + 4y + y2 = 41 + -41 Combine like terms: 41 + -41 = 0 -41 + 4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 4y + 41 + y2 = 0 + 41 Reorder the terms: -41 + 41 + 4y + y2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 4y + y2 = 0 + 41 4y + y2 = 0 + 41 Combine like terms: 0 + 41 = 41 4y + y2 = 41 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 41 + 4 Reorder the terms: 4 + 4y + y2 = 41 + 4 Combine like terms: 41 + 4 = 45 4 + 4y + y2 = 45 Factor a perfect square on the left side: (y + 2)(y + 2) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (y + 2) equal to 6.708203933 and -6.708203933.Subproblem 1
y + 2 = 6.708203933 Simplifying y + 2 = 6.708203933 Reorder the terms: 2 + y = 6.708203933 Solving 2 + y = 6.708203933 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + y = 6.708203933 + -2 y = 6.708203933 + -2 Combine like terms: 6.708203933 + -2 = 4.708203933 y = 4.708203933 Simplifying y = 4.708203933Subproblem 2
y + 2 = -6.708203933 Simplifying y + 2 = -6.708203933 Reorder the terms: 2 + y = -6.708203933 Solving 2 + y = -6.708203933 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + y = -6.708203933 + -2 y = -6.708203933 + -2 Combine like terms: -6.708203933 + -2 = -8.708203933 y = -8.708203933 Simplifying y = -8.708203933Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.708203933, -8.708203933}
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