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Simplifying 2 + y(y + -5) = 0 Reorder the terms: 2 + y(-5 + y) = 0 2 + (-5 * y + y * y) = 0 2 + (-5y + y2) = 0 Solving 2 + -5y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -5y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + -5y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5y + y2 = 0 + -2 -5y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -5y + y2 = -2 The y term is -5y. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y + 6.25 + y2 = -2 + 6.25 Reorder the terms: 6.25 + -5y + y2 = -2 + 6.25 Combine like terms: -2 + 6.25 = 4.25 6.25 + -5y + y2 = 4.25 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (y + -2.5) equal to 2.061552813 and -2.061552813.Subproblem 1
y + -2.5 = 2.061552813 Simplifying y + -2.5 = 2.061552813 Reorder the terms: -2.5 + y = 2.061552813 Solving -2.5 + y = 2.061552813 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 2.061552813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 2.061552813 + 2.5 y = 2.061552813 + 2.5 Combine like terms: 2.061552813 + 2.5 = 4.561552813 y = 4.561552813 Simplifying y = 4.561552813Subproblem 2
y + -2.5 = -2.061552813 Simplifying y + -2.5 = -2.061552813 Reorder the terms: -2.5 + y = -2.061552813 Solving -2.5 + y = -2.061552813 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = -2.061552813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -2.061552813 + 2.5 y = -2.061552813 + 2.5 Combine like terms: -2.061552813 + 2.5 = 0.438447187 y = 0.438447187 Simplifying y = 0.438447187Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.561552813, 0.438447187}
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