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Simplifying -8y2 = -12 + -1y4 Solving -8y2 = -12 + -1y4 Solving for variable 'y'. Reorder the terms: 12 + -8y2 + y4 = -12 + -1y4 + 12 + y4 Reorder the terms: 12 + -8y2 + y4 = -12 + 12 + -1y4 + y4 Combine like terms: -12 + 12 = 0 12 + -8y2 + y4 = 0 + -1y4 + y4 12 + -8y2 + y4 = -1y4 + y4 Combine like terms: -1y4 + y4 = 0 12 + -8y2 + y4 = 0 Factor a trinomial. (2 + -1y2)(6 + -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 '(6 + -1y2)' equal to zero and attempt to solve: Simplifying 6 + -1y2 = 0 Solving 6 + -1y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1y2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1y2 = 0 + -6 -1y2 = 0 + -6 Combine like terms: 0 + -6 = -6 -1y2 = -6 Divide each side by '-1'. y2 = 6 Simplifying y2 = 6 Take the square root of each side: y = {-2.449489743, 2.449489743}Solution
y = {-1.414213562, 1.414213562, -2.449489743, 2.449489743}
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