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Simplifying (4y2 + 9)(16y2 + 0.25) = 0 Reorder the terms: (9 + 4y2)(16y2 + 0.25) = 0 Reorder the terms: (9 + 4y2)(0.25 + 16y2) = 0 Multiply (9 + 4y2) * (0.25 + 16y2) (9(0.25 + 16y2) + 4y2 * (0.25 + 16y2)) = 0 ((0.25 * 9 + 16y2 * 9) + 4y2 * (0.25 + 16y2)) = 0 ((2.25 + 144y2) + 4y2 * (0.25 + 16y2)) = 0 (2.25 + 144y2 + (0.25 * 4y2 + 16y2 * 4y2)) = 0 (2.25 + 144y2 + (1y2 + 64y4)) = 0 Combine like terms: 144y2 + 1y2 = 145y2 (2.25 + 145y2 + 64y4) = 0 Solving 2.25 + 145y2 + 64y4 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. 0.03515625 + 2.265625y2 + y4 = 0 Move the constant term to the right: Add '-0.03515625' to each side of the equation. 0.03515625 + 2.265625y2 + -0.03515625 + y4 = 0 + -0.03515625 Reorder the terms: 0.03515625 + -0.03515625 + 2.265625y2 + y4 = 0 + -0.03515625 Combine like terms: 0.03515625 + -0.03515625 = 0.00000000 0.00000000 + 2.265625y2 + y4 = 0 + -0.03515625 2.265625y2 + y4 = 0 + -0.03515625 Combine like terms: 0 + -0.03515625 = -0.03515625 2.265625y2 + y4 = -0.03515625 The y term is 2.265625y2. Take half its coefficient (1.1328125). Square it (1.283264160) and add it to both sides. Add '1.283264160' to each side of the equation. 2.265625y2 + 1.283264160 + y4 = -0.03515625 + 1.283264160 Reorder the terms: 1.283264160 + 2.265625y2 + y4 = -0.03515625 + 1.283264160 Combine like terms: -0.03515625 + 1.283264160 = 1.24810791 1.283264160 + 2.265625y2 + y4 = 1.24810791 Factor a perfect square on the left side: (y2 + 1.1328125)(y2 + 1.1328125) = 1.24810791 Calculate the square root of the right side: 1.1171875 Break this problem into two subproblems by setting (y2 + 1.1328125) equal to 1.1171875 and -1.1171875.Subproblem 1
y2 + 1.1328125 = 1.1171875 Simplifying y2 + 1.1328125 = 1.1171875 Reorder the terms: 1.1328125 + y2 = 1.1171875 Solving 1.1328125 + y2 = 1.1171875 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.1328125' to each side of the equation. 1.1328125 + -1.1328125 + y2 = 1.1171875 + -1.1328125 Combine like terms: 1.1328125 + -1.1328125 = 0.0000000 0.0000000 + y2 = 1.1171875 + -1.1328125 y2 = 1.1171875 + -1.1328125 Combine like terms: 1.1171875 + -1.1328125 = -0.015625 y2 = -0.015625 Simplifying y2 = -0.015625 Reorder the terms: 0.015625 + y2 = -0.015625 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.015625 + y2 = 0.000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
y2 + 1.1328125 = -1.1171875 Simplifying y2 + 1.1328125 = -1.1171875 Reorder the terms: 1.1328125 + y2 = -1.1171875 Solving 1.1328125 + y2 = -1.1171875 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.1328125' to each side of the equation. 1.1328125 + -1.1328125 + y2 = -1.1171875 + -1.1328125 Combine like terms: 1.1328125 + -1.1328125 = 0.0000000 0.0000000 + y2 = -1.1171875 + -1.1328125 y2 = -1.1171875 + -1.1328125 Combine like terms: -1.1171875 + -1.1328125 = -2.25 y2 = -2.25 Simplifying y2 = -2.25 Reorder the terms: 2.25 + y2 = -2.25 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 2.25 + y2 = 0.00 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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