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Simplifying y4 + -12y2 + 9 = 0 Reorder the terms: 9 + -12y2 + y4 = 0 Solving 9 + -12y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -12y2 + -9 + y4 = 0 + -9 Reorder the terms: 9 + -9 + -12y2 + y4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -12y2 + y4 = 0 + -9 -12y2 + y4 = 0 + -9 Combine like terms: 0 + -9 = -9 -12y2 + y4 = -9 The y term is -12y2. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y2 + 36 + y4 = -9 + 36 Reorder the terms: 36 + -12y2 + y4 = -9 + 36 Combine like terms: -9 + 36 = 27 36 + -12y2 + y4 = 27 Factor a perfect square on the left side: (y2 + -6)(y2 + -6) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (y2 + -6) equal to 5.196152423 and -5.196152423.Subproblem 1
y2 + -6 = 5.196152423 Simplifying y2 + -6 = 5.196152423 Reorder the terms: -6 + y2 = 5.196152423 Solving -6 + y2 = 5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y2 = 5.196152423 + 6 Combine like terms: -6 + 6 = 0 0 + y2 = 5.196152423 + 6 y2 = 5.196152423 + 6 Combine like terms: 5.196152423 + 6 = 11.196152423 y2 = 11.196152423 Simplifying y2 = 11.196152423 Take the square root of each side: y = {-3.346065215, 3.346065215}Subproblem 2
y2 + -6 = -5.196152423 Simplifying y2 + -6 = -5.196152423 Reorder the terms: -6 + y2 = -5.196152423 Solving -6 + y2 = -5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y2 = -5.196152423 + 6 Combine like terms: -6 + 6 = 0 0 + y2 = -5.196152423 + 6 y2 = -5.196152423 + 6 Combine like terms: -5.196152423 + 6 = 0.803847577 y2 = 0.803847577 Simplifying y2 = 0.803847577 Take the square root of each side: y = {-0.896575472, 0.896575472}Solution
The solution to the problem is based on the solutions from the subproblems. y = {-3.346065215, 3.346065215, -0.896575472, 0.896575472}
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