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Simplifying (5y2 + -1)(5y2 + 1) = 0 Reorder the terms: (-1 + 5y2)(5y2 + 1) = 0 Reorder the terms: (-1 + 5y2)(1 + 5y2) = 0 Multiply (-1 + 5y2) * (1 + 5y2) (-1(1 + 5y2) + 5y2 * (1 + 5y2)) = 0 ((1 * -1 + 5y2 * -1) + 5y2 * (1 + 5y2)) = 0 ((-1 + -5y2) + 5y2 * (1 + 5y2)) = 0 (-1 + -5y2 + (1 * 5y2 + 5y2 * 5y2)) = 0 (-1 + -5y2 + (5y2 + 25y4)) = 0 Combine like terms: -5y2 + 5y2 = 0 (-1 + 0 + 25y4) = 0 (-1 + 25y4) = 0 Solving -1 + 25y4 = 0 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 + 25y4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 25y4 = 0 + 1 25y4 = 0 + 1 Combine like terms: 0 + 1 = 1 25y4 = 1 Divide each side by '25'. y4 = 0.04 Simplifying y4 = 0.04 Reorder the terms: -0.04 + y4 = 0.04 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 -0.04 + y4 = 0.00 Factor a difference between two squares. (0.2 + y2)(-0.2 + y2) = 0.00Subproblem 1
Set the factor '(0.2 + y2)' equal to zero and attempt to solve: Simplifying 0.2 + y2 = 0 Solving 0.2 + y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + y2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + y2 = 0 + -0.2 y2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 y2 = -0.2 Simplifying y2 = -0.2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-0.2 + y2)' equal to zero and attempt to solve: Simplifying -0.2 + y2 = 0 Solving -0.2 + y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + y2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + y2 = 0 + 0.2 y2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 y2 = 0.2 Simplifying y2 = 0.2 Take the square root of each side: y = {-0.447213596, 0.447213596}Solution
y = {-0.447213596, 0.447213596}
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