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Simplifying y4 + -12.5y2 + 39.0625 = 0 Reorder the terms: 39.0625 + -12.5y2 + y4 = 0 Solving 39.0625 + -12.5y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-39.0625' to each side of the equation. 39.0625 + -12.5y2 + -39.0625 + y4 = 0 + -39.0625 Reorder the terms: 39.0625 + -39.0625 + -12.5y2 + y4 = 0 + -39.0625 Combine like terms: 39.0625 + -39.0625 = 0.0000 0.0000 + -12.5y2 + y4 = 0 + -39.0625 -12.5y2 + y4 = 0 + -39.0625 Combine like terms: 0 + -39.0625 = -39.0625 -12.5y2 + y4 = -39.0625 The y term is -12.5y2. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5y2 + 39.0625 + y4 = -39.0625 + 39.0625 Reorder the terms: 39.0625 + -12.5y2 + y4 = -39.0625 + 39.0625 Combine like terms: -39.0625 + 39.0625 = 0.0000 39.0625 + -12.5y2 + y4 = 0.0000 Factor a perfect square on the left side: (y2 + -6.25)(y2 + -6.25) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (y2 + -6.25) equal to 0.0000 and 0.0000.Subproblem 1
y2 + -6.25 = 0.0000 Simplifying y2 + -6.25 = 0.0000 Reorder the terms: -6.25 + y2 = 0.0000 Solving -6.25 + y2 = 0.0000 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + y2 = 0.0000 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + y2 = 0.0000 + 6.25 y2 = 0.0000 + 6.25 Combine like terms: 0.0000 + 6.25 = 6.25 y2 = 6.25 Simplifying y2 = 6.25 Take the square root of each side: y = {-2.5, 2.5}Subproblem 2
y2 + -6.25 = 0.0000 Simplifying y2 + -6.25 = 0.0000 Reorder the terms: -6.25 + y2 = 0.0000 Solving -6.25 + y2 = 0.0000 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + y2 = 0.0000 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + y2 = 0.0000 + 6.25 y2 = 0.0000 + 6.25 Combine like terms: 0.0000 + 6.25 = 6.25 y2 = 6.25 Simplifying y2 = 6.25 Take the square root of each side: y = {-2.5, 2.5}Solution
The solution to the problem is based on the solutions from the subproblems. y = {-2.5, 2.5, -2.5, 2.5}
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