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Simplifying 7x4 + 23x2 + 3 = 0 Reorder the terms: 3 + 23x2 + 7x4 = 0 Solving 3 + 23x2 + 7x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.4285714286 + 3.285714286x2 + x4 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + 3.285714286x2 + -0.4285714286 + x4 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + 3.285714286x2 + x4 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + 3.285714286x2 + x4 = 0 + -0.4285714286 3.285714286x2 + x4 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 3.285714286x2 + x4 = -0.4285714286 The x term is 3.285714286x2. Take half its coefficient (1.642857143). Square it (2.698979592) and add it to both sides. Add '2.698979592' to each side of the equation. 3.285714286x2 + 2.698979592 + x4 = -0.4285714286 + 2.698979592 Reorder the terms: 2.698979592 + 3.285714286x2 + x4 = -0.4285714286 + 2.698979592 Combine like terms: -0.4285714286 + 2.698979592 = 2.2704081634 2.698979592 + 3.285714286x2 + x4 = 2.2704081634 Factor a perfect square on the left side: (x2 + 1.642857143)(x2 + 1.642857143) = 2.2704081634 Calculate the square root of the right side: 1.506787365 Break this problem into two subproblems by setting (x2 + 1.642857143) equal to 1.506787365 and -1.506787365.Subproblem 1
x2 + 1.642857143 = 1.506787365 Simplifying x2 + 1.642857143 = 1.506787365 Reorder the terms: 1.642857143 + x2 = 1.506787365 Solving 1.642857143 + x2 = 1.506787365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.642857143' to each side of the equation. 1.642857143 + -1.642857143 + x2 = 1.506787365 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x2 = 1.506787365 + -1.642857143 x2 = 1.506787365 + -1.642857143 Combine like terms: 1.506787365 + -1.642857143 = -0.136069778 x2 = -0.136069778 Simplifying x2 = -0.136069778 Reorder the terms: 0.136069778 + x2 = -0.136069778 + 0.136069778 Combine like terms: -0.136069778 + 0.136069778 = 0.000000000 0.136069778 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 1.642857143 = -1.506787365 Simplifying x2 + 1.642857143 = -1.506787365 Reorder the terms: 1.642857143 + x2 = -1.506787365 Solving 1.642857143 + x2 = -1.506787365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.642857143' to each side of the equation. 1.642857143 + -1.642857143 + x2 = -1.506787365 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x2 = -1.506787365 + -1.642857143 x2 = -1.506787365 + -1.642857143 Combine like terms: -1.506787365 + -1.642857143 = -3.149644508 x2 = -3.149644508 Simplifying x2 = -3.149644508 Reorder the terms: 3.149644508 + x2 = -3.149644508 + 3.149644508 Combine like terms: -3.149644508 + 3.149644508 = 0.000000000 3.149644508 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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