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Simplifying x4 = 47x2 + -98 Reorder the terms: x4 = -98 + 47x2 Solving x4 = -98 + 47x2 Solving for variable 'x'. Reorder the terms: 98 + -47x2 + x4 = -98 + 47x2 + 98 + -47x2 Reorder the terms: 98 + -47x2 + x4 = -98 + 98 + 47x2 + -47x2 Combine like terms: -98 + 98 = 0 98 + -47x2 + x4 = 0 + 47x2 + -47x2 98 + -47x2 + x4 = 47x2 + -47x2 Combine like terms: 47x2 + -47x2 = 0 98 + -47x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-98' to each side of the equation. 98 + -47x2 + -98 + x4 = 0 + -98 Reorder the terms: 98 + -98 + -47x2 + x4 = 0 + -98 Combine like terms: 98 + -98 = 0 0 + -47x2 + x4 = 0 + -98 -47x2 + x4 = 0 + -98 Combine like terms: 0 + -98 = -98 -47x2 + x4 = -98 The x term is -47x2. Take half its coefficient (-23.5). Square it (552.25) and add it to both sides. Add '552.25' to each side of the equation. -47x2 + 552.25 + x4 = -98 + 552.25 Reorder the terms: 552.25 + -47x2 + x4 = -98 + 552.25 Combine like terms: -98 + 552.25 = 454.25 552.25 + -47x2 + x4 = 454.25 Factor a perfect square on the left side: (x2 + -23.5)(x2 + -23.5) = 454.25 Calculate the square root of the right side: 21.313141486 Break this problem into two subproblems by setting (x2 + -23.5) equal to 21.313141486 and -21.313141486.Subproblem 1
x2 + -23.5 = 21.313141486 Simplifying x2 + -23.5 = 21.313141486 Reorder the terms: -23.5 + x2 = 21.313141486 Solving -23.5 + x2 = 21.313141486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.5' to each side of the equation. -23.5 + 23.5 + x2 = 21.313141486 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + x2 = 21.313141486 + 23.5 x2 = 21.313141486 + 23.5 Combine like terms: 21.313141486 + 23.5 = 44.813141486 x2 = 44.813141486 Simplifying x2 = 44.813141486 Take the square root of each side: x = {-6.694261833, 6.694261833}Subproblem 2
x2 + -23.5 = -21.313141486 Simplifying x2 + -23.5 = -21.313141486 Reorder the terms: -23.5 + x2 = -21.313141486 Solving -23.5 + x2 = -21.313141486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.5' to each side of the equation. -23.5 + 23.5 + x2 = -21.313141486 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + x2 = -21.313141486 + 23.5 x2 = -21.313141486 + 23.5 Combine like terms: -21.313141486 + 23.5 = 2.186858514 x2 = 2.186858514 Simplifying x2 = 2.186858514 Take the square root of each side: x = {-1.478803068, 1.478803068}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.694261833, 6.694261833, -1.478803068, 1.478803068}
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