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Simplifying 2y2 + 4y + -24 = 0 Reorder the terms: -24 + 4y + 2y2 = 0 Solving -24 + 4y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 2y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 2y + y2)' equal to zero and attempt to solve: Simplifying -12 + 2y + y2 = 0 Solving -12 + 2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 2y + 12 + y2 = 0 + 12 Reorder the terms: -12 + 12 + 2y + y2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 2y + y2 = 0 + 12 2y + y2 = 0 + 12 Combine like terms: 0 + 12 = 12 2y + y2 = 12 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 12 + 1 Reorder the terms: 1 + 2y + y2 = 12 + 1 Combine like terms: 12 + 1 = 13 1 + 2y + y2 = 13 Factor a perfect square on the left side: (y + 1)(y + 1) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (y + 1) equal to 3.605551275 and -3.605551275.Subproblem 1
y + 1 = 3.605551275 Simplifying y + 1 = 3.605551275 Reorder the terms: 1 + y = 3.605551275 Solving 1 + y = 3.605551275 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 3.605551275 + -1 Combine like terms: 1 + -1 = 0 0 + y = 3.605551275 + -1 y = 3.605551275 + -1 Combine like terms: 3.605551275 + -1 = 2.605551275 y = 2.605551275 Simplifying y = 2.605551275Subproblem 2
y + 1 = -3.605551275 Simplifying y + 1 = -3.605551275 Reorder the terms: 1 + y = -3.605551275 Solving 1 + y = -3.605551275 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -3.605551275 + -1 Combine like terms: 1 + -1 = 0 0 + y = -3.605551275 + -1 y = -3.605551275 + -1 Combine like terms: -3.605551275 + -1 = -4.605551275 y = -4.605551275 Simplifying y = -4.605551275Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.605551275, -4.605551275}Solution
y = {2.605551275, -4.605551275}
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