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Simplifying 2y2 + -24y = 94 Reorder the terms: -24y + 2y2 = 94 Solving -24y + 2y2 = 94 Solving for variable 'y'. Reorder the terms: -94 + -24y + 2y2 = 94 + -94 Combine like terms: 94 + -94 = 0 -94 + -24y + 2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-47 + -12y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-47 + -12y + y2)' equal to zero and attempt to solve: Simplifying -47 + -12y + y2 = 0 Solving -47 + -12y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -12y + 47 + y2 = 0 + 47 Reorder the terms: -47 + 47 + -12y + y2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -12y + y2 = 0 + 47 -12y + y2 = 0 + 47 Combine like terms: 0 + 47 = 47 -12y + y2 = 47 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = 47 + 36 Reorder the terms: 36 + -12y + y2 = 47 + 36 Combine like terms: 47 + 36 = 83 36 + -12y + y2 = 83 Factor a perfect square on the left side: (y + -6)(y + -6) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (y + -6) equal to 9.110433579 and -9.110433579.Subproblem 1
y + -6 = 9.110433579 Simplifying y + -6 = 9.110433579 Reorder the terms: -6 + y = 9.110433579 Solving -6 + y = 9.110433579 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 9.110433579 + 6 Combine like terms: -6 + 6 = 0 0 + y = 9.110433579 + 6 y = 9.110433579 + 6 Combine like terms: 9.110433579 + 6 = 15.110433579 y = 15.110433579 Simplifying y = 15.110433579Subproblem 2
y + -6 = -9.110433579 Simplifying y + -6 = -9.110433579 Reorder the terms: -6 + y = -9.110433579 Solving -6 + y = -9.110433579 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -9.110433579 + 6 Combine like terms: -6 + 6 = 0 0 + y = -9.110433579 + 6 y = -9.110433579 + 6 Combine like terms: -9.110433579 + 6 = -3.110433579 y = -3.110433579 Simplifying y = -3.110433579Solution
The solution to the problem is based on the solutions from the subproblems. y = {15.110433579, -3.110433579}Solution
y = {15.110433579, -3.110433579}
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