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Simplifying 2y2 + -12y + -44 = 0 Reorder the terms: -44 + -12y + 2y2 = 0 Solving -44 + -12y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-22 + -6y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-22 + -6y + y2)' equal to zero and attempt to solve: Simplifying -22 + -6y + y2 = 0 Solving -22 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -6y + 22 + y2 = 0 + 22 Reorder the terms: -22 + 22 + -6y + y2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -6y + y2 = 0 + 22 -6y + y2 = 0 + 22 Combine like terms: 0 + 22 = 22 -6y + y2 = 22 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = 22 + 9 Reorder the terms: 9 + -6y + y2 = 22 + 9 Combine like terms: 22 + 9 = 31 9 + -6y + y2 = 31 Factor a perfect square on the left side: (y + -3)(y + -3) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (y + -3) equal to 5.567764363 and -5.567764363.Subproblem 1
y + -3 = 5.567764363 Simplifying y + -3 = 5.567764363 Reorder the terms: -3 + y = 5.567764363 Solving -3 + y = 5.567764363 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 5.567764363 + 3 Combine like terms: -3 + 3 = 0 0 + y = 5.567764363 + 3 y = 5.567764363 + 3 Combine like terms: 5.567764363 + 3 = 8.567764363 y = 8.567764363 Simplifying y = 8.567764363Subproblem 2
y + -3 = -5.567764363 Simplifying y + -3 = -5.567764363 Reorder the terms: -3 + y = -5.567764363 Solving -3 + y = -5.567764363 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -5.567764363 + 3 Combine like terms: -3 + 3 = 0 0 + y = -5.567764363 + 3 y = -5.567764363 + 3 Combine like terms: -5.567764363 + 3 = -2.567764363 y = -2.567764363 Simplifying y = -2.567764363Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.567764363, -2.567764363}Solution
y = {8.567764363, -2.567764363}
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