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Simplifying (y + -7)(y + 7) = 9y Reorder the terms: (-7 + y)(y + 7) = 9y Reorder the terms: (-7 + y)(7 + y) = 9y Multiply (-7 + y) * (7 + y) (-7(7 + y) + y(7 + y)) = 9y ((7 * -7 + y * -7) + y(7 + y)) = 9y ((-49 + -7y) + y(7 + y)) = 9y (-49 + -7y + (7 * y + y * y)) = 9y (-49 + -7y + (7y + y2)) = 9y Combine like terms: -7y + 7y = 0 (-49 + 0 + y2) = 9y (-49 + y2) = 9y Solving -49 + y2 = 9y Solving for variable 'y'. Reorder the terms: -49 + -9y + y2 = 9y + -9y Combine like terms: 9y + -9y = 0 -49 + -9y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -9y + 49 + y2 = 0 + 49 Reorder the terms: -49 + 49 + -9y + y2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -9y + y2 = 0 + 49 -9y + y2 = 0 + 49 Combine like terms: 0 + 49 = 49 -9y + y2 = 49 The y term is -9y. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9y + 20.25 + y2 = 49 + 20.25 Reorder the terms: 20.25 + -9y + y2 = 49 + 20.25 Combine like terms: 49 + 20.25 = 69.25 20.25 + -9y + y2 = 69.25 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 69.25 Calculate the square root of the right side: 8.321658489 Break this problem into two subproblems by setting (y + -4.5) equal to 8.321658489 and -8.321658489.Subproblem 1
y + -4.5 = 8.321658489 Simplifying y + -4.5 = 8.321658489 Reorder the terms: -4.5 + y = 8.321658489 Solving -4.5 + y = 8.321658489 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = 8.321658489 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 8.321658489 + 4.5 y = 8.321658489 + 4.5 Combine like terms: 8.321658489 + 4.5 = 12.821658489 y = 12.821658489 Simplifying y = 12.821658489Subproblem 2
y + -4.5 = -8.321658489 Simplifying y + -4.5 = -8.321658489 Reorder the terms: -4.5 + y = -8.321658489 Solving -4.5 + y = -8.321658489 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = -8.321658489 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -8.321658489 + 4.5 y = -8.321658489 + 4.5 Combine like terms: -8.321658489 + 4.5 = -3.821658489 y = -3.821658489 Simplifying y = -3.821658489Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.821658489, -3.821658489}
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