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Simplifying y2 + -6y + -9 = 4y + -12 Reorder the terms: -9 + -6y + y2 = 4y + -12 Reorder the terms: -9 + -6y + y2 = -12 + 4y Solving -9 + -6y + y2 = -12 + 4y Solving for variable 'y'. Reorder the terms: -9 + 12 + -6y + -4y + y2 = -12 + 4y + 12 + -4y Combine like terms: -9 + 12 = 3 3 + -6y + -4y + y2 = -12 + 4y + 12 + -4y Combine like terms: -6y + -4y = -10y 3 + -10y + y2 = -12 + 4y + 12 + -4y Reorder the terms: 3 + -10y + y2 = -12 + 12 + 4y + -4y Combine like terms: -12 + 12 = 0 3 + -10y + y2 = 0 + 4y + -4y 3 + -10y + y2 = 4y + -4y Combine like terms: 4y + -4y = 0 3 + -10y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -10y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + -10y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -10y + y2 = 0 + -3 -10y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 -10y + y2 = -3 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = -3 + 25 Reorder the terms: 25 + -10y + y2 = -3 + 25 Combine like terms: -3 + 25 = 22 25 + -10y + y2 = 22 Factor a perfect square on the left side: (y + -5)(y + -5) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (y + -5) equal to 4.69041576 and -4.69041576.Subproblem 1
y + -5 = 4.69041576 Simplifying y + -5 = 4.69041576 Reorder the terms: -5 + y = 4.69041576 Solving -5 + y = 4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + y = 4.69041576 + 5 y = 4.69041576 + 5 Combine like terms: 4.69041576 + 5 = 9.69041576 y = 9.69041576 Simplifying y = 9.69041576Subproblem 2
y + -5 = -4.69041576 Simplifying y + -5 = -4.69041576 Reorder the terms: -5 + y = -4.69041576 Solving -5 + y = -4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + y = -4.69041576 + 5 y = -4.69041576 + 5 Combine like terms: -4.69041576 + 5 = 0.30958424 y = 0.30958424 Simplifying y = 0.30958424Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.69041576, 0.30958424}
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