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Simplifying 25 + -60y + y2 = 0 Solving 25 + -60y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -60y + -25 + y2 = 0 + -25 Reorder the terms: 25 + -25 + -60y + y2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -60y + y2 = 0 + -25 -60y + y2 = 0 + -25 Combine like terms: 0 + -25 = -25 -60y + y2 = -25 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 = -25 + 900 Reorder the terms: 900 + -60y + y2 = -25 + 900 Combine like terms: -25 + 900 = 875 900 + -60y + y2 = 875 Factor a perfect square on the left side: (y + -30)(y + -30) = 875 Calculate the square root of the right side: 29.580398915 Break this problem into two subproblems by setting (y + -30) equal to 29.580398915 and -29.580398915.Subproblem 1
y + -30 = 29.580398915 Simplifying y + -30 = 29.580398915 Reorder the terms: -30 + y = 29.580398915 Solving -30 + y = 29.580398915 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 = 29.580398915 + 30 Combine like terms: -30 + 30 = 0 0 + y = 29.580398915 + 30 y = 29.580398915 + 30 Combine like terms: 29.580398915 + 30 = 59.580398915 y = 59.580398915 Simplifying y = 59.580398915Subproblem 2
y + -30 = -29.580398915 Simplifying y + -30 = -29.580398915 Reorder the terms: -30 + y = -29.580398915 Solving -30 + y = -29.580398915 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 = -29.580398915 + 30 Combine like terms: -30 + 30 = 0 0 + y = -29.580398915 + 30 y = -29.580398915 + 30 Combine like terms: -29.580398915 + 30 = 0.419601085 y = 0.419601085 Simplifying y = 0.419601085Solution
The solution to the problem is based on the solutions from the subproblems. y = {59.580398915, 0.419601085}
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