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Simplifying y + -14y3 + -1y5 = 0 Solving y + -14y3 + -1y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(1 + -14y2 + -1y4) = 0Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(1 + -14y2 + -1y4)' equal to zero and attempt to solve: Simplifying 1 + -14y2 + -1y4 = 0 Solving 1 + -14y2 + -1y4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + 14y2 + y4 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 14y2 + 1 + y4 = 0 + 1 Reorder the terms: -1 + 1 + 14y2 + y4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 14y2 + y4 = 0 + 1 14y2 + y4 = 0 + 1 Combine like terms: 0 + 1 = 1 14y2 + y4 = 1 The y term is 14y2. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14y2 + 49 + y4 = 1 + 49 Reorder the terms: 49 + 14y2 + y4 = 1 + 49 Combine like terms: 1 + 49 = 50 49 + 14y2 + y4 = 50 Factor a perfect square on the left side: (y2 + 7)(y2 + 7) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (y2 + 7) equal to 7.071067812 and -7.071067812.Subproblem 1
y2 + 7 = 7.071067812 Simplifying y2 + 7 = 7.071067812 Reorder the terms: 7 + y2 = 7.071067812 Solving 7 + y2 = 7.071067812 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y2 = 7.071067812 + -7 Combine like terms: 7 + -7 = 0 0 + y2 = 7.071067812 + -7 y2 = 7.071067812 + -7 Combine like terms: 7.071067812 + -7 = 0.071067812 y2 = 0.071067812 Simplifying y2 = 0.071067812 Take the square root of each side: y = {-0.266585468, 0.266585468}Subproblem 2
y2 + 7 = -7.071067812 Simplifying y2 + 7 = -7.071067812 Reorder the terms: 7 + y2 = -7.071067812 Solving 7 + y2 = -7.071067812 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y2 = -7.071067812 + -7 Combine like terms: 7 + -7 = 0 0 + y2 = -7.071067812 + -7 y2 = -7.071067812 + -7 Combine like terms: -7.071067812 + -7 = -14.071067812 y2 = -14.071067812 Simplifying y2 = -14.071067812 Reorder the terms: 14.071067812 + y2 = -14.071067812 + 14.071067812 Combine like terms: -14.071067812 + 14.071067812 = 0.000000000 14.071067812 + 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.Solution
y = {0}
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