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Simplifying 0.25y4 + 29y2 + -9 = 0 Reorder the terms: -9 + 29y2 + 0.25y4 = 0 Solving -9 + 29y2 + 0.25y4 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -36 + 116y2 + y4 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 116y2 + 36 + y4 = 0 + 36 Reorder the terms: -36 + 36 + 116y2 + y4 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 116y2 + y4 = 0 + 36 116y2 + y4 = 0 + 36 Combine like terms: 0 + 36 = 36 116y2 + y4 = 36 The y term is 116y2. Take half its coefficient (58). Square it (3364) and add it to both sides. Add '3364' to each side of the equation. 116y2 + 3364 + y4 = 36 + 3364 Reorder the terms: 3364 + 116y2 + y4 = 36 + 3364 Combine like terms: 36 + 3364 = 3400 3364 + 116y2 + y4 = 3400 Factor a perfect square on the left side: (y2 + 58)(y2 + 58) = 3400 Calculate the square root of the right side: 58.309518948 Break this problem into two subproblems by setting (y2 + 58) equal to 58.309518948 and -58.309518948.Subproblem 1
y2 + 58 = 58.309518948 Simplifying y2 + 58 = 58.309518948 Reorder the terms: 58 + y2 = 58.309518948 Solving 58 + y2 = 58.309518948 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-58' to each side of the equation. 58 + -58 + y2 = 58.309518948 + -58 Combine like terms: 58 + -58 = 0 0 + y2 = 58.309518948 + -58 y2 = 58.309518948 + -58 Combine like terms: 58.309518948 + -58 = 0.309518948 y2 = 0.309518948 Simplifying y2 = 0.309518948 Take the square root of each side: y = {-0.556344271, 0.556344271}Subproblem 2
y2 + 58 = -58.309518948 Simplifying y2 + 58 = -58.309518948 Reorder the terms: 58 + y2 = -58.309518948 Solving 58 + y2 = -58.309518948 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-58' to each side of the equation. 58 + -58 + y2 = -58.309518948 + -58 Combine like terms: 58 + -58 = 0 0 + y2 = -58.309518948 + -58 y2 = -58.309518948 + -58 Combine like terms: -58.309518948 + -58 = -116.309518948 y2 = -116.309518948 Simplifying y2 = -116.309518948 Reorder the terms: 116.309518948 + y2 = -116.309518948 + 116.309518948 Combine like terms: -116.309518948 + 116.309518948 = 0.000000000 116.309518948 + 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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