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Simplifying (-4y4) + -1(4y2) + 1 = 0 Remove parenthesis around (4y2) (-4y4) + -1 * 4y2 + 1 = 0 Multiply -1 * 4 (-4y4) + -4y2 + 1 = 0 Reorder the terms: 1 + -4y2 + (-4y4) = 0 Solving 1 + -4y2 + (-4y4) = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + y2 + y4 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + y2 + 0.25 + y4 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + y2 + y4 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + y2 + y4 = 0 + 0.25 y2 + y4 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 y2 + y4 = 0.25 The y term is y2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + y4 = 0.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + y4 = 0.25 + 0.25 Combine like terms: 0.25 + 0.25 = 0.5 1.25 + y4 = 0.5 Factor a perfect square on the left side: ((y2) + 0.5)((y2) + 0.5) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting ((y2) + 0.5) equal to 0.707106781 and -0.707106781.Subproblem 1
(y2) + 0.5 = 0.707106781 Simplifying (y2) + 0.5 = 0.707106781 y2 + 0.5 = 0.707106781 Reorder the terms: 0.5 + y2 = 0.707106781 Solving 0.5 + y2 = 0.707106781 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y2 = 0.707106781 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y2 = 0.707106781 + -0.5 y2 = 0.707106781 + -0.5 Combine like terms: 0.707106781 + -0.5 = 0.207106781 y2 = 0.207106781 Simplifying y2 = 0.207106781 Take the square root of each side: y = {-0.45508986, 0.45508986}Subproblem 2
(y2) + 0.5 = -0.707106781 Simplifying (y2) + 0.5 = -0.707106781 y2 + 0.5 = -0.707106781 Reorder the terms: 0.5 + y2 = -0.707106781 Solving 0.5 + y2 = -0.707106781 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y2 = -0.707106781 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y2 = -0.707106781 + -0.5 y2 = -0.707106781 + -0.5 Combine like terms: -0.707106781 + -0.5 = -1.207106781 y2 = -1.207106781 Simplifying y2 = -1.207106781 Reorder the terms: 1.207106781 + y2 = -1.207106781 + 1.207106781 Combine like terms: -1.207106781 + 1.207106781 = 0.000000000 1.207106781 + 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.
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