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Simplifying 81y4 + -1 = 18y2 Reorder the terms: -1 + 81y4 = 18y2 Solving -1 + 81y4 = 18y2 Solving for variable 'y'. Reorder the terms: -1 + -18y2 + 81y4 = 18y2 + -18y2 Combine like terms: 18y2 + -18y2 = 0 -1 + -18y2 + 81y4 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.01234567901 + -0.2222222222y2 + y4 = 0 Move the constant term to the right: Add '0.01234567901' to each side of the equation. -0.01234567901 + -0.2222222222y2 + 0.01234567901 + y4 = 0 + 0.01234567901 Reorder the terms: -0.01234567901 + 0.01234567901 + -0.2222222222y2 + y4 = 0 + 0.01234567901 Combine like terms: -0.01234567901 + 0.01234567901 = 0.00000000000 0.00000000000 + -0.2222222222y2 + y4 = 0 + 0.01234567901 -0.2222222222y2 + y4 = 0 + 0.01234567901 Combine like terms: 0 + 0.01234567901 = 0.01234567901 -0.2222222222y2 + y4 = 0.01234567901 The y term is -0.2222222222y2. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222y2 + 0.01234567901 + y4 = 0.01234567901 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222y2 + y4 = 0.01234567901 + 0.01234567901 Combine like terms: 0.01234567901 + 0.01234567901 = 0.02469135802 0.01234567901 + -0.2222222222y2 + y4 = 0.02469135802 Factor a perfect square on the left side: (y2 + -0.1111111111)(y2 + -0.1111111111) = 0.02469135802 Calculate the square root of the right side: 0.15713484 Break this problem into two subproblems by setting (y2 + -0.1111111111) equal to 0.15713484 and -0.15713484.Subproblem 1
y2 + -0.1111111111 = 0.15713484 Simplifying y2 + -0.1111111111 = 0.15713484 Reorder the terms: -0.1111111111 + y2 = 0.15713484 Solving -0.1111111111 + y2 = 0.15713484 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + y2 = 0.15713484 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + y2 = 0.15713484 + 0.1111111111 y2 = 0.15713484 + 0.1111111111 Combine like terms: 0.15713484 + 0.1111111111 = 0.2682459511 y2 = 0.2682459511 Simplifying y2 = 0.2682459511 Take the square root of each side: y = {-0.517924658, 0.517924658}Subproblem 2
y2 + -0.1111111111 = -0.15713484 Simplifying y2 + -0.1111111111 = -0.15713484 Reorder the terms: -0.1111111111 + y2 = -0.15713484 Solving -0.1111111111 + y2 = -0.15713484 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + y2 = -0.15713484 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + y2 = -0.15713484 + 0.1111111111 y2 = -0.15713484 + 0.1111111111 Combine like terms: -0.15713484 + 0.1111111111 = -0.0460237289 y2 = -0.0460237289 Simplifying y2 = -0.0460237289 Reorder the terms: 0.0460237289 + y2 = -0.0460237289 + 0.0460237289 Combine like terms: -0.0460237289 + 0.0460237289 = 0.0000000000 0.0460237289 + y2 = 0.0000000000 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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