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Simplifying 4y4 + -32y2 + -400 = 0 Reorder the terms: -400 + -32y2 + 4y4 = 0 Solving -400 + -32y2 + 4y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(-100 + -8y2 + y4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-100 + -8y2 + y4)' equal to zero and attempt to solve: Simplifying -100 + -8y2 + y4 = 0 Solving -100 + -8y2 + y4 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -8y2 + 100 + y4 = 0 + 100 Reorder the terms: -100 + 100 + -8y2 + y4 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -8y2 + y4 = 0 + 100 -8y2 + y4 = 0 + 100 Combine like terms: 0 + 100 = 100 -8y2 + y4 = 100 The y term is -8y2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y2 + 16 + y4 = 100 + 16 Reorder the terms: 16 + -8y2 + y4 = 100 + 16 Combine like terms: 100 + 16 = 116 16 + -8y2 + y4 = 116 Factor a perfect square on the left side: (y2 + -4)(y2 + -4) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (y2 + -4) equal to 10.770329614 and -10.770329614.Subproblem 1
y2 + -4 = 10.770329614 Simplifying y2 + -4 = 10.770329614 Reorder the terms: -4 + y2 = 10.770329614 Solving -4 + y2 = 10.770329614 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 + y2 = 10.770329614 + 4 Combine like terms: -4 + 4 = 0 0 + y2 = 10.770329614 + 4 y2 = 10.770329614 + 4 Combine like terms: 10.770329614 + 4 = 14.770329614 y2 = 14.770329614 Simplifying y2 = 14.770329614 Take the square root of each side: y = {-3.843218653, 3.843218653}Subproblem 2
y2 + -4 = -10.770329614 Simplifying y2 + -4 = -10.770329614 Reorder the terms: -4 + y2 = -10.770329614 Solving -4 + y2 = -10.770329614 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 + y2 = -10.770329614 + 4 Combine like terms: -4 + 4 = 0 0 + y2 = -10.770329614 + 4 y2 = -10.770329614 + 4 Combine like terms: -10.770329614 + 4 = -6.770329614 y2 = -6.770329614 Simplifying y2 = -6.770329614 Reorder the terms: 6.770329614 + y2 = -6.770329614 + 6.770329614 Combine like terms: -6.770329614 + 6.770329614 = 0.000000000 6.770329614 + y2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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