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Simplifying x4 + -14x2 + 9 = 0 Reorder the terms: 9 + -14x2 + x4 = 0 Solving 9 + -14x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -14x2 + -9 + x4 = 0 + -9 Reorder the terms: 9 + -9 + -14x2 + x4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -14x2 + x4 = 0 + -9 -14x2 + x4 = 0 + -9 Combine like terms: 0 + -9 = -9 -14x2 + x4 = -9 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 = -9 + 49 Reorder the terms: 49 + -14x2 + x4 = -9 + 49 Combine like terms: -9 + 49 = 40 49 + -14x2 + x4 = 40 Factor a perfect square on the left side: (x2 + -7)(x2 + -7) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x2 + -7) equal to 6.32455532 and -6.32455532.Subproblem 1
x2 + -7 = 6.32455532 Simplifying x2 + -7 = 6.32455532 Reorder the terms: -7 + x2 = 6.32455532 Solving -7 + x2 = 6.32455532 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 = 6.32455532 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = 6.32455532 + 7 x2 = 6.32455532 + 7 Combine like terms: 6.32455532 + 7 = 13.32455532 x2 = 13.32455532 Simplifying x2 = 13.32455532 Take the square root of each side: x = {-3.65028154, 3.65028154}Subproblem 2
x2 + -7 = -6.32455532 Simplifying x2 + -7 = -6.32455532 Reorder the terms: -7 + x2 = -6.32455532 Solving -7 + x2 = -6.32455532 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 = -6.32455532 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = -6.32455532 + 7 x2 = -6.32455532 + 7 Combine like terms: -6.32455532 + 7 = 0.67544468 x2 = 0.67544468 Simplifying x2 = 0.67544468 Take the square root of each side: x = {-0.821854415, 0.821854415}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.65028154, 3.65028154, -0.821854415, 0.821854415}
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