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Simplifying y2 + 25y + -10 = 0 Reorder the terms: -10 + 25y + y2 = 0 Solving -10 + 25y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 25y + 10 + y2 = 0 + 10 Reorder the terms: -10 + 10 + 25y + y2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 25y + y2 = 0 + 10 25y + y2 = 0 + 10 Combine like terms: 0 + 10 = 10 25y + y2 = 10 The y term is 25y. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25y + 156.25 + y2 = 10 + 156.25 Reorder the terms: 156.25 + 25y + y2 = 10 + 156.25 Combine like terms: 10 + 156.25 = 166.25 156.25 + 25y + y2 = 166.25 Factor a perfect square on the left side: (y + 12.5)(y + 12.5) = 166.25 Calculate the square root of the right side: 12.893796958 Break this problem into two subproblems by setting (y + 12.5) equal to 12.893796958 and -12.893796958.Subproblem 1
y + 12.5 = 12.893796958 Simplifying y + 12.5 = 12.893796958 Reorder the terms: 12.5 + y = 12.893796958 Solving 12.5 + y = 12.893796958 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + y = 12.893796958 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + y = 12.893796958 + -12.5 y = 12.893796958 + -12.5 Combine like terms: 12.893796958 + -12.5 = 0.393796958 y = 0.393796958 Simplifying y = 0.393796958Subproblem 2
y + 12.5 = -12.893796958 Simplifying y + 12.5 = -12.893796958 Reorder the terms: 12.5 + y = -12.893796958 Solving 12.5 + y = -12.893796958 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + y = -12.893796958 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + y = -12.893796958 + -12.5 y = -12.893796958 + -12.5 Combine like terms: -12.893796958 + -12.5 = -25.393796958 y = -25.393796958 Simplifying y = -25.393796958Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.393796958, -25.393796958}
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