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Simplifying 2y2 + -8y + 16 = 52 Reorder the terms: 16 + -8y + 2y2 = 52 Solving 16 + -8y + 2y2 = 52 Solving for variable 'y'. Reorder the terms: 16 + -52 + -8y + 2y2 = 52 + -52 Combine like terms: 16 + -52 = -36 -36 + -8y + 2y2 = 52 + -52 Combine like terms: 52 + -52 = 0 -36 + -8y + 2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + -4y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + -4y + y2)' equal to zero and attempt to solve: Simplifying -18 + -4y + y2 = 0 Solving -18 + -4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -4y + 18 + y2 = 0 + 18 Reorder the terms: -18 + 18 + -4y + y2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -4y + y2 = 0 + 18 -4y + y2 = 0 + 18 Combine like terms: 0 + 18 = 18 -4y + y2 = 18 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 18 + 4 Reorder the terms: 4 + -4y + y2 = 18 + 4 Combine like terms: 18 + 4 = 22 4 + -4y + y2 = 22 Factor a perfect square on the left side: (y + -2)(y + -2) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (y + -2) equal to 4.69041576 and -4.69041576.Subproblem 1
y + -2 = 4.69041576 Simplifying y + -2 = 4.69041576 Reorder the terms: -2 + y = 4.69041576 Solving -2 + y = 4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 4.69041576 + 2 Combine like terms: -2 + 2 = 0 0 + y = 4.69041576 + 2 y = 4.69041576 + 2 Combine like terms: 4.69041576 + 2 = 6.69041576 y = 6.69041576 Simplifying y = 6.69041576Subproblem 2
y + -2 = -4.69041576 Simplifying y + -2 = -4.69041576 Reorder the terms: -2 + y = -4.69041576 Solving -2 + y = -4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -4.69041576 + 2 Combine like terms: -2 + 2 = 0 0 + y = -4.69041576 + 2 y = -4.69041576 + 2 Combine like terms: -4.69041576 + 2 = -2.69041576 y = -2.69041576 Simplifying y = -2.69041576Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.69041576, -2.69041576}Solution
y = {6.69041576, -2.69041576}
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