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Simplifying x4 + -61x2 + 98 = 0 Reorder the terms: 98 + -61x2 + x4 = 0 Solving 98 + -61x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-98' to each side of the equation. 98 + -61x2 + -98 + x4 = 0 + -98 Reorder the terms: 98 + -98 + -61x2 + x4 = 0 + -98 Combine like terms: 98 + -98 = 0 0 + -61x2 + x4 = 0 + -98 -61x2 + x4 = 0 + -98 Combine like terms: 0 + -98 = -98 -61x2 + x4 = -98 The x term is -61x2. Take half its coefficient (-30.5). Square it (930.25) and add it to both sides. Add '930.25' to each side of the equation. -61x2 + 930.25 + x4 = -98 + 930.25 Reorder the terms: 930.25 + -61x2 + x4 = -98 + 930.25 Combine like terms: -98 + 930.25 = 832.25 930.25 + -61x2 + x4 = 832.25 Factor a perfect square on the left side: (x2 + -30.5)(x2 + -30.5) = 832.25 Calculate the square root of the right side: 28.848743474 Break this problem into two subproblems by setting (x2 + -30.5) equal to 28.848743474 and -28.848743474.Subproblem 1
x2 + -30.5 = 28.848743474 Simplifying x2 + -30.5 = 28.848743474 Reorder the terms: -30.5 + x2 = 28.848743474 Solving -30.5 + x2 = 28.848743474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30.5' to each side of the equation. -30.5 + 30.5 + x2 = 28.848743474 + 30.5 Combine like terms: -30.5 + 30.5 = 0.0 0.0 + x2 = 28.848743474 + 30.5 x2 = 28.848743474 + 30.5 Combine like terms: 28.848743474 + 30.5 = 59.348743474 x2 = 59.348743474 Simplifying x2 = 59.348743474 Take the square root of each side: x = {-7.703813567, 7.703813567}Subproblem 2
x2 + -30.5 = -28.848743474 Simplifying x2 + -30.5 = -28.848743474 Reorder the terms: -30.5 + x2 = -28.848743474 Solving -30.5 + x2 = -28.848743474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30.5' to each side of the equation. -30.5 + 30.5 + x2 = -28.848743474 + 30.5 Combine like terms: -30.5 + 30.5 = 0.0 0.0 + x2 = -28.848743474 + 30.5 x2 = -28.848743474 + 30.5 Combine like terms: -28.848743474 + 30.5 = 1.651256526 x2 = 1.651256526 Simplifying x2 = 1.651256526 Take the square root of each side: x = {-1.285012267, 1.285012267}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.703813567, 7.703813567, -1.285012267, 1.285012267}
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