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Simplifying y2 + -7y + -9 = 0 Reorder the terms: -9 + -7y + y2 = 0 Solving -9 + -7y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -7y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + -7y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -7y + y2 = 0 + 9 -7y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 -7y + y2 = 9 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 = 9 + 12.25 Reorder the terms: 12.25 + -7y + y2 = 9 + 12.25 Combine like terms: 9 + 12.25 = 21.25 12.25 + -7y + y2 = 21.25 Factor a perfect square on the left side: (y + -3.5)(y + -3.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (y + -3.5) equal to 4.609772229 and -4.609772229.Subproblem 1
y + -3.5 = 4.609772229 Simplifying y + -3.5 = 4.609772229 Reorder the terms: -3.5 + y = 4.609772229 Solving -3.5 + y = 4.609772229 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 = 4.609772229 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 4.609772229 + 3.5 y = 4.609772229 + 3.5 Combine like terms: 4.609772229 + 3.5 = 8.109772229 y = 8.109772229 Simplifying y = 8.109772229Subproblem 2
y + -3.5 = -4.609772229 Simplifying y + -3.5 = -4.609772229 Reorder the terms: -3.5 + y = -4.609772229 Solving -3.5 + y = -4.609772229 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 = -4.609772229 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = -4.609772229 + 3.5 y = -4.609772229 + 3.5 Combine like terms: -4.609772229 + 3.5 = -1.109772229 y = -1.109772229 Simplifying y = -1.109772229Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.109772229, -1.109772229}
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