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Simplifying (2 + -1y2)(2 + -1y2) = 0 Multiply (2 + -1y2) * (2 + -1y2) (2(2 + -1y2) + -1y2 * (2 + -1y2)) = 0 ((2 * 2 + -1y2 * 2) + -1y2 * (2 + -1y2)) = 0 ((4 + -2y2) + -1y2 * (2 + -1y2)) = 0 (4 + -2y2 + (2 * -1y2 + -1y2 * -1y2)) = 0 (4 + -2y2 + (-2y2 + 1y4)) = 0 Combine like terms: -2y2 + -2y2 = -4y2 (4 + -4y2 + 1y4) = 0 Solving 4 + -4y2 + 1y4 = 0 Solving for variable 'y'. Factor a trinomial. (2 + -1y2)(2 + -1y2) = 0Subproblem 1
Set the factor '(2 + -1y2)' equal to zero and attempt to solve: Simplifying 2 + -1y2 = 0 Solving 2 + -1y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y2 = 0 + -2 -1y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1y2 = -2 Divide each side by '-1'. y2 = 2 Simplifying y2 = 2 Take the square root of each side: y = {-1.414213562, 1.414213562}Subproblem 2
Set the factor '(2 + -1y2)' equal to zero and attempt to solve: Simplifying 2 + -1y2 = 0 Solving 2 + -1y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y2 = 0 + -2 -1y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1y2 = -2 Divide each side by '-1'. y2 = 2 Simplifying y2 = 2 Take the square root of each side: y = {-1.414213562, 1.414213562}Solution
y = {-1.414213562, 1.414213562, -1.414213562, 1.414213562}
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