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Simplifying 2y2 + -32y + 8 = 0 Reorder the terms: 8 + -32y + 2y2 = 0 Solving 8 + -32y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -16y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -16y + y2)' equal to zero and attempt to solve: Simplifying 4 + -16y + y2 = 0 Solving 4 + -16y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -16y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + -16y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -16y + y2 = 0 + -4 -16y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 -16y + y2 = -4 The y term is -16y. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16y + 64 + y2 = -4 + 64 Reorder the terms: 64 + -16y + y2 = -4 + 64 Combine like terms: -4 + 64 = 60 64 + -16y + y2 = 60 Factor a perfect square on the left side: (y + -8)(y + -8) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (y + -8) equal to 7.745966692 and -7.745966692.Subproblem 1
y + -8 = 7.745966692 Simplifying y + -8 = 7.745966692 Reorder the terms: -8 + y = 7.745966692 Solving -8 + y = 7.745966692 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + y = 7.745966692 + 8 Combine like terms: -8 + 8 = 0 0 + y = 7.745966692 + 8 y = 7.745966692 + 8 Combine like terms: 7.745966692 + 8 = 15.745966692 y = 15.745966692 Simplifying y = 15.745966692Subproblem 2
y + -8 = -7.745966692 Simplifying y + -8 = -7.745966692 Reorder the terms: -8 + y = -7.745966692 Solving -8 + y = -7.745966692 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + y = -7.745966692 + 8 Combine like terms: -8 + 8 = 0 0 + y = -7.745966692 + 8 y = -7.745966692 + 8 Combine like terms: -7.745966692 + 8 = 0.254033308 y = 0.254033308 Simplifying y = 0.254033308Solution
The solution to the problem is based on the solutions from the subproblems. y = {15.745966692, 0.254033308}Solution
y = {15.745966692, 0.254033308}
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