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Simplifying x4 + -14x2 + 47 = 0 Reorder the terms: 47 + -14x2 + x4 = 0 Solving 47 + -14x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + -14x2 + -47 + x4 = 0 + -47 Reorder the terms: 47 + -47 + -14x2 + x4 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + -14x2 + x4 = 0 + -47 -14x2 + x4 = 0 + -47 Combine like terms: 0 + -47 = -47 -14x2 + x4 = -47 The x term is -14x2. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x2 + 49 + x4 = -47 + 49 Reorder the terms: 49 + -14x2 + x4 = -47 + 49 Combine like terms: -47 + 49 = 2 49 + -14x2 + x4 = 2 Factor a perfect square on the left side: (x2 + -7)(x2 + -7) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x2 + -7) equal to 1.414213562 and -1.414213562.Subproblem 1
x2 + -7 = 1.414213562 Simplifying x2 + -7 = 1.414213562 Reorder the terms: -7 + x2 = 1.414213562 Solving -7 + x2 = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = 1.414213562 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = 1.414213562 + 7 x2 = 1.414213562 + 7 Combine like terms: 1.414213562 + 7 = 8.414213562 x2 = 8.414213562 Simplifying x2 = 8.414213562 Take the square root of each side: x = {-2.900726385, 2.900726385}Subproblem 2
x2 + -7 = -1.414213562 Simplifying x2 + -7 = -1.414213562 Reorder the terms: -7 + x2 = -1.414213562 Solving -7 + x2 = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = -1.414213562 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = -1.414213562 + 7 x2 = -1.414213562 + 7 Combine like terms: -1.414213562 + 7 = 5.585786438 x2 = 5.585786438 Simplifying x2 = 5.585786438 Take the square root of each side: x = {-2.363426842, 2.363426842}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.900726385, 2.900726385, -2.363426842, 2.363426842}
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