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Simplifying 5y + y2 = 25 Solving 5y + y2 = 25 Solving for variable 'y'. Reorder the terms: -25 + 5y + y2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 5y + 25 + y2 = 0 + 25 Reorder the terms: -25 + 25 + 5y + y2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 5y + y2 = 0 + 25 5y + y2 = 0 + 25 Combine like terms: 0 + 25 = 25 5y + y2 = 25 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 = 25 + 6.25 Reorder the terms: 6.25 + 5y + y2 = 25 + 6.25 Combine like terms: 25 + 6.25 = 31.25 6.25 + 5y + y2 = 31.25 Factor a perfect square on the left side: (y + 2.5)(y + 2.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (y + 2.5) equal to 5.590169944 and -5.590169944.Subproblem 1
y + 2.5 = 5.590169944 Simplifying y + 2.5 = 5.590169944 Reorder the terms: 2.5 + y = 5.590169944 Solving 2.5 + y = 5.590169944 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 = 5.590169944 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = 5.590169944 + -2.5 y = 5.590169944 + -2.5 Combine like terms: 5.590169944 + -2.5 = 3.090169944 y = 3.090169944 Simplifying y = 3.090169944Subproblem 2
y + 2.5 = -5.590169944 Simplifying y + 2.5 = -5.590169944 Reorder the terms: 2.5 + y = -5.590169944 Solving 2.5 + y = -5.590169944 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 = -5.590169944 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = -5.590169944 + -2.5 y = -5.590169944 + -2.5 Combine like terms: -5.590169944 + -2.5 = -8.090169944 y = -8.090169944 Simplifying y = -8.090169944Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.090169944, -8.090169944}
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