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Simplifying 2y2 + 16y + -12 = 0 Reorder the terms: -12 + 16y + 2y2 = 0 Solving -12 + 16y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 8y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 8y + y2)' equal to zero and attempt to solve: Simplifying -6 + 8y + y2 = 0 Solving -6 + 8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 8y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + 8y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 8y + y2 = 0 + 6 8y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 8y + y2 = 6 The y term is 8y. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8y + 16 + y2 = 6 + 16 Reorder the terms: 16 + 8y + y2 = 6 + 16 Combine like terms: 6 + 16 = 22 16 + 8y + y2 = 22 Factor a perfect square on the left side: (y + 4)(y + 4) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (y + 4) equal to 4.69041576 and -4.69041576.Subproblem 1
y + 4 = 4.69041576 Simplifying y + 4 = 4.69041576 Reorder the terms: 4 + y = 4.69041576 Solving 4 + y = 4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 4.69041576 + -4 Combine like terms: 4 + -4 = 0 0 + y = 4.69041576 + -4 y = 4.69041576 + -4 Combine like terms: 4.69041576 + -4 = 0.69041576 y = 0.69041576 Simplifying y = 0.69041576Subproblem 2
y + 4 = -4.69041576 Simplifying y + 4 = -4.69041576 Reorder the terms: 4 + y = -4.69041576 Solving 4 + y = -4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = -4.69041576 + -4 Combine like terms: 4 + -4 = 0 0 + y = -4.69041576 + -4 y = -4.69041576 + -4 Combine like terms: -4.69041576 + -4 = -8.69041576 y = -8.69041576 Simplifying y = -8.69041576Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.69041576, -8.69041576}Solution
y = {0.69041576, -8.69041576}
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