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Simplifying y4 + -100y2 + 36 = 0 Reorder the terms: 36 + -100y2 + y4 = 0 Solving 36 + -100y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -100y2 + -36 + y4 = 0 + -36 Reorder the terms: 36 + -36 + -100y2 + y4 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -100y2 + y4 = 0 + -36 -100y2 + y4 = 0 + -36 Combine like terms: 0 + -36 = -36 -100y2 + y4 = -36 The y term is -100y2. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100y2 + 2500 + y4 = -36 + 2500 Reorder the terms: 2500 + -100y2 + y4 = -36 + 2500 Combine like terms: -36 + 2500 = 2464 2500 + -100y2 + y4 = 2464 Factor a perfect square on the left side: (y2 + -50)(y2 + -50) = 2464 Calculate the square root of the right side: 49.638694584 Break this problem into two subproblems by setting (y2 + -50) equal to 49.638694584 and -49.638694584.Subproblem 1
y2 + -50 = 49.638694584 Simplifying y2 + -50 = 49.638694584 Reorder the terms: -50 + y2 = 49.638694584 Solving -50 + y2 = 49.638694584 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + y2 = 49.638694584 + 50 Combine like terms: -50 + 50 = 0 0 + y2 = 49.638694584 + 50 y2 = 49.638694584 + 50 Combine like terms: 49.638694584 + 50 = 99.638694584 y2 = 99.638694584 Simplifying y2 = 99.638694584 Take the square root of each side: y = {-9.981918382, 9.981918382}Subproblem 2
y2 + -50 = -49.638694584 Simplifying y2 + -50 = -49.638694584 Reorder the terms: -50 + y2 = -49.638694584 Solving -50 + y2 = -49.638694584 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + y2 = -49.638694584 + 50 Combine like terms: -50 + 50 = 0 0 + y2 = -49.638694584 + 50 y2 = -49.638694584 + 50 Combine like terms: -49.638694584 + 50 = 0.361305416 y2 = 0.361305416 Simplifying y2 = 0.361305416 Take the square root of each side: y = {-0.601086862, 0.601086862}Solution
The solution to the problem is based on the solutions from the subproblems. y = {-9.981918382, 9.981918382, -0.601086862, 0.601086862}
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