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Simplifying x4 + -6x2 + 3 = 0 Reorder the terms: 3 + -6x2 + x4 = 0 Solving 3 + -6x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -6x2 + -3 + x4 = 0 + -3 Reorder the terms: 3 + -3 + -6x2 + x4 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -6x2 + x4 = 0 + -3 -6x2 + x4 = 0 + -3 Combine like terms: 0 + -3 = -3 -6x2 + x4 = -3 The x term is -6x2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x2 + 9 + x4 = -3 + 9 Reorder the terms: 9 + -6x2 + x4 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + -6x2 + x4 = 6 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x2 + -3) equal to 2.449489743 and -2.449489743.Subproblem 1
x2 + -3 = 2.449489743 Simplifying x2 + -3 = 2.449489743 Reorder the terms: -3 + x2 = 2.449489743 Solving -3 + x2 = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = 2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 2.449489743 + 3 x2 = 2.449489743 + 3 Combine like terms: 2.449489743 + 3 = 5.449489743 x2 = 5.449489743 Simplifying x2 = 5.449489743 Take the square root of each side: x = {-2.334414218, 2.334414218}Subproblem 2
x2 + -3 = -2.449489743 Simplifying x2 + -3 = -2.449489743 Reorder the terms: -3 + x2 = -2.449489743 Solving -3 + x2 = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = -2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -2.449489743 + 3 x2 = -2.449489743 + 3 Combine like terms: -2.449489743 + 3 = 0.550510257 x2 = 0.550510257 Simplifying x2 = 0.550510257 Take the square root of each side: x = {-0.741963784, 0.741963784}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.334414218, 2.334414218, -0.741963784, 0.741963784}
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