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Simplifying y2 + 60y + 54 = 0 Reorder the terms: 54 + 60y + y2 = 0 Solving 54 + 60y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-54' to each side of the equation. 54 + 60y + -54 + y2 = 0 + -54 Reorder the terms: 54 + -54 + 60y + y2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + 60y + y2 = 0 + -54 60y + y2 = 0 + -54 Combine like terms: 0 + -54 = -54 60y + y2 = -54 The y term is 60y. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60y + 900 + y2 = -54 + 900 Reorder the terms: 900 + 60y + y2 = -54 + 900 Combine like terms: -54 + 900 = 846 900 + 60y + y2 = 846 Factor a perfect square on the left side: (y + 30)(y + 30) = 846 Calculate the square root of the right side: 29.086079144 Break this problem into two subproblems by setting (y + 30) equal to 29.086079144 and -29.086079144.Subproblem 1
y + 30 = 29.086079144 Simplifying y + 30 = 29.086079144 Reorder the terms: 30 + y = 29.086079144 Solving 30 + y = 29.086079144 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + y = 29.086079144 + -30 Combine like terms: 30 + -30 = 0 0 + y = 29.086079144 + -30 y = 29.086079144 + -30 Combine like terms: 29.086079144 + -30 = -0.913920856 y = -0.913920856 Simplifying y = -0.913920856Subproblem 2
y + 30 = -29.086079144 Simplifying y + 30 = -29.086079144 Reorder the terms: 30 + y = -29.086079144 Solving 30 + y = -29.086079144 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + y = -29.086079144 + -30 Combine like terms: 30 + -30 = 0 0 + y = -29.086079144 + -30 y = -29.086079144 + -30 Combine like terms: -29.086079144 + -30 = -59.086079144 y = -59.086079144 Simplifying y = -59.086079144Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.913920856, -59.086079144}
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