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Simplifying x4 + -26x2 + 9 = 0 Reorder the terms: 9 + -26x2 + x4 = 0 Solving 9 + -26x2 + 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 + -26x2 + -9 + x4 = 0 + -9 Reorder the terms: 9 + -9 + -26x2 + x4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -26x2 + x4 = 0 + -9 -26x2 + x4 = 0 + -9 Combine like terms: 0 + -9 = -9 -26x2 + x4 = -9 The x term is -26x2. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x2 + 169 + x4 = -9 + 169 Reorder the terms: 169 + -26x2 + x4 = -9 + 169 Combine like terms: -9 + 169 = 160 169 + -26x2 + x4 = 160 Factor a perfect square on the left side: (x2 + -13)(x2 + -13) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (x2 + -13) equal to 12.649110641 and -12.649110641.Subproblem 1
x2 + -13 = 12.649110641 Simplifying x2 + -13 = 12.649110641 Reorder the terms: -13 + x2 = 12.649110641 Solving -13 + x2 = 12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x2 = 12.649110641 + 13 Combine like terms: -13 + 13 = 0 0 + x2 = 12.649110641 + 13 x2 = 12.649110641 + 13 Combine like terms: 12.649110641 + 13 = 25.649110641 x2 = 25.649110641 Simplifying x2 = 25.649110641 Take the square root of each side: x = {-5.064495102, 5.064495102}Subproblem 2
x2 + -13 = -12.649110641 Simplifying x2 + -13 = -12.649110641 Reorder the terms: -13 + x2 = -12.649110641 Solving -13 + x2 = -12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x2 = -12.649110641 + 13 Combine like terms: -13 + 13 = 0 0 + x2 = -12.649110641 + 13 x2 = -12.649110641 + 13 Combine like terms: -12.649110641 + 13 = 0.350889359 x2 = 0.350889359 Simplifying x2 = 0.350889359 Take the square root of each side: x = {-0.592359147, 0.592359147}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.064495102, 5.064495102, -0.592359147, 0.592359147}
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