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Simplifying (y + -7)(y + 4) = 6y Reorder the terms: (-7 + y)(y + 4) = 6y Reorder the terms: (-7 + y)(4 + y) = 6y Multiply (-7 + y) * (4 + y) (-7(4 + y) + y(4 + y)) = 6y ((4 * -7 + y * -7) + y(4 + y)) = 6y ((-28 + -7y) + y(4 + y)) = 6y (-28 + -7y + (4 * y + y * y)) = 6y (-28 + -7y + (4y + y2)) = 6y Combine like terms: -7y + 4y = -3y (-28 + -3y + y2) = 6y Solving -28 + -3y + y2 = 6y Solving for variable 'y'. Reorder the terms: -28 + -3y + -6y + y2 = 6y + -6y Combine like terms: -3y + -6y = -9y -28 + -9y + y2 = 6y + -6y Combine like terms: 6y + -6y = 0 -28 + -9y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -9y + 28 + y2 = 0 + 28 Reorder the terms: -28 + 28 + -9y + y2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -9y + y2 = 0 + 28 -9y + y2 = 0 + 28 Combine like terms: 0 + 28 = 28 -9y + y2 = 28 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 = 28 + 20.25 Reorder the terms: 20.25 + -9y + y2 = 28 + 20.25 Combine like terms: 28 + 20.25 = 48.25 20.25 + -9y + y2 = 48.25 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (y + -4.5) equal to 6.946221995 and -6.946221995.Subproblem 1
y + -4.5 = 6.946221995 Simplifying y + -4.5 = 6.946221995 Reorder the terms: -4.5 + y = 6.946221995 Solving -4.5 + y = 6.946221995 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 = 6.946221995 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 6.946221995 + 4.5 y = 6.946221995 + 4.5 Combine like terms: 6.946221995 + 4.5 = 11.446221995 y = 11.446221995 Simplifying y = 11.446221995Subproblem 2
y + -4.5 = -6.946221995 Simplifying y + -4.5 = -6.946221995 Reorder the terms: -4.5 + y = -6.946221995 Solving -4.5 + y = -6.946221995 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 = -6.946221995 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -6.946221995 + 4.5 y = -6.946221995 + 4.5 Combine like terms: -6.946221995 + 4.5 = -2.446221995 y = -2.446221995 Simplifying y = -2.446221995Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.446221995, -2.446221995}
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