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Simplifying y2 + 15y + -3 = 0 Reorder the terms: -3 + 15y + y2 = 0 Solving -3 + 15y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 15y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + 15y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 15y + y2 = 0 + 3 15y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 15y + y2 = 3 The y term is 15y. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15y + 56.25 + y2 = 3 + 56.25 Reorder the terms: 56.25 + 15y + y2 = 3 + 56.25 Combine like terms: 3 + 56.25 = 59.25 56.25 + 15y + y2 = 59.25 Factor a perfect square on the left side: (y + 7.5)(y + 7.5) = 59.25 Calculate the square root of the right side: 7.697402159 Break this problem into two subproblems by setting (y + 7.5) equal to 7.697402159 and -7.697402159.Subproblem 1
y + 7.5 = 7.697402159 Simplifying y + 7.5 = 7.697402159 Reorder the terms: 7.5 + y = 7.697402159 Solving 7.5 + y = 7.697402159 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + y = 7.697402159 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + y = 7.697402159 + -7.5 y = 7.697402159 + -7.5 Combine like terms: 7.697402159 + -7.5 = 0.197402159 y = 0.197402159 Simplifying y = 0.197402159Subproblem 2
y + 7.5 = -7.697402159 Simplifying y + 7.5 = -7.697402159 Reorder the terms: 7.5 + y = -7.697402159 Solving 7.5 + y = -7.697402159 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + y = -7.697402159 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + y = -7.697402159 + -7.5 y = -7.697402159 + -7.5 Combine like terms: -7.697402159 + -7.5 = -15.197402159 y = -15.197402159 Simplifying y = -15.197402159Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.197402159, -15.197402159}
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