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Simplifying y2 + 7y = 49 Reorder the terms: 7y + y2 = 49 Solving 7y + y2 = 49 Solving for variable 'y'. Reorder the terms: -49 + 7y + y2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + 7y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 7y + 49 + y2 = 0 + 49 Reorder the terms: -49 + 49 + 7y + y2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 7y + y2 = 0 + 49 7y + y2 = 0 + 49 Combine like terms: 0 + 49 = 49 7y + y2 = 49 The y term is 7y. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7y + 12.25 + y2 = 49 + 12.25 Reorder the terms: 12.25 + 7y + y2 = 49 + 12.25 Combine like terms: 49 + 12.25 = 61.25 12.25 + 7y + y2 = 61.25 Factor a perfect square on the left side: (y + 3.5)(y + 3.5) = 61.25 Calculate the square root of the right side: 7.826237921 Break this problem into two subproblems by setting (y + 3.5) equal to 7.826237921 and -7.826237921.Subproblem 1
y + 3.5 = 7.826237921 Simplifying y + 3.5 = 7.826237921 Reorder the terms: 3.5 + y = 7.826237921 Solving 3.5 + y = 7.826237921 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = 7.826237921 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 7.826237921 + -3.5 y = 7.826237921 + -3.5 Combine like terms: 7.826237921 + -3.5 = 4.326237921 y = 4.326237921 Simplifying y = 4.326237921Subproblem 2
y + 3.5 = -7.826237921 Simplifying y + 3.5 = -7.826237921 Reorder the terms: 3.5 + y = -7.826237921 Solving 3.5 + y = -7.826237921 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = -7.826237921 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -7.826237921 + -3.5 y = -7.826237921 + -3.5 Combine like terms: -7.826237921 + -3.5 = -11.326237921 y = -11.326237921 Simplifying y = -11.326237921Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.326237921, -11.326237921}
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