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Simplifying 39x4 + 34x2 + -26 = 0 Reorder the terms: -26 + 34x2 + 39x4 = 0 Solving -26 + 34x2 + 39x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 39 the coefficient of the squared term: Divide each side by '39'. -0.6666666667 + 0.8717948718x2 + x4 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 0.8717948718x2 + 0.6666666667 + x4 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 0.8717948718x2 + x4 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 0.8717948718x2 + x4 = 0 + 0.6666666667 0.8717948718x2 + x4 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 0.8717948718x2 + x4 = 0.6666666667 The x term is 0.8717948718x2. Take half its coefficient (0.4358974359). Square it (0.1900065746) and add it to both sides. Add '0.1900065746' to each side of the equation. 0.8717948718x2 + 0.1900065746 + x4 = 0.6666666667 + 0.1900065746 Reorder the terms: 0.1900065746 + 0.8717948718x2 + x4 = 0.6666666667 + 0.1900065746 Combine like terms: 0.6666666667 + 0.1900065746 = 0.8566732413 0.1900065746 + 0.8717948718x2 + x4 = 0.8566732413 Factor a perfect square on the left side: (x2 + 0.4358974359)(x2 + 0.4358974359) = 0.8566732413 Calculate the square root of the right side: 0.925566443 Break this problem into two subproblems by setting (x2 + 0.4358974359) equal to 0.925566443 and -0.925566443.Subproblem 1
x2 + 0.4358974359 = 0.925566443 Simplifying x2 + 0.4358974359 = 0.925566443 Reorder the terms: 0.4358974359 + x2 = 0.925566443 Solving 0.4358974359 + x2 = 0.925566443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4358974359' to each side of the equation. 0.4358974359 + -0.4358974359 + x2 = 0.925566443 + -0.4358974359 Combine like terms: 0.4358974359 + -0.4358974359 = 0.0000000000 0.0000000000 + x2 = 0.925566443 + -0.4358974359 x2 = 0.925566443 + -0.4358974359 Combine like terms: 0.925566443 + -0.4358974359 = 0.4896690071 x2 = 0.4896690071 Simplifying x2 = 0.4896690071 Take the square root of each side: x = {-0.699763537, 0.699763537}Subproblem 2
x2 + 0.4358974359 = -0.925566443 Simplifying x2 + 0.4358974359 = -0.925566443 Reorder the terms: 0.4358974359 + x2 = -0.925566443 Solving 0.4358974359 + x2 = -0.925566443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4358974359' to each side of the equation. 0.4358974359 + -0.4358974359 + x2 = -0.925566443 + -0.4358974359 Combine like terms: 0.4358974359 + -0.4358974359 = 0.0000000000 0.0000000000 + x2 = -0.925566443 + -0.4358974359 x2 = -0.925566443 + -0.4358974359 Combine like terms: -0.925566443 + -0.4358974359 = -1.3614638789 x2 = -1.3614638789 Simplifying x2 = -1.3614638789 Reorder the terms: 1.3614638789 + x2 = -1.3614638789 + 1.3614638789 Combine like terms: -1.3614638789 + 1.3614638789 = 0.0000000000 1.3614638789 + x2 = 0.0000000000 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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