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Simplifying 11x2 + 7x4 + -1 = 0 Reorder the terms: -1 + 11x2 + 7x4 = 0 Solving -1 + 11x2 + 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'. -0.1428571429 + 1.571428571x2 + x4 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + 1.571428571x2 + 0.1428571429 + x4 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + 1.571428571x2 + x4 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + 1.571428571x2 + x4 = 0 + 0.1428571429 1.571428571x2 + x4 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 1.571428571x2 + x4 = 0.1428571429 The x term is 1.571428571x2. Take half its coefficient (0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. 1.571428571x2 + 0.6173469384 + x4 = 0.1428571429 + 0.6173469384 Reorder the terms: 0.6173469384 + 1.571428571x2 + x4 = 0.1428571429 + 0.6173469384 Combine like terms: 0.1428571429 + 0.6173469384 = 0.7602040813 0.6173469384 + 1.571428571x2 + x4 = 0.7602040813 Factor a perfect square on the left side: (x2 + 0.7857142855)(x2 + 0.7857142855) = 0.7602040813 Calculate the square root of the right side: 0.87189683 Break this problem into two subproblems by setting (x2 + 0.7857142855) equal to 0.87189683 and -0.87189683.Subproblem 1
x2 + 0.7857142855 = 0.87189683 Simplifying x2 + 0.7857142855 = 0.87189683 Reorder the terms: 0.7857142855 + x2 = 0.87189683 Solving 0.7857142855 + x2 = 0.87189683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x2 = 0.87189683 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x2 = 0.87189683 + -0.7857142855 x2 = 0.87189683 + -0.7857142855 Combine like terms: 0.87189683 + -0.7857142855 = 0.0861825445 x2 = 0.0861825445 Simplifying x2 = 0.0861825445 Take the square root of each side: x = {-0.293568637, 0.293568637}Subproblem 2
x2 + 0.7857142855 = -0.87189683 Simplifying x2 + 0.7857142855 = -0.87189683 Reorder the terms: 0.7857142855 + x2 = -0.87189683 Solving 0.7857142855 + x2 = -0.87189683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x2 = -0.87189683 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x2 = -0.87189683 + -0.7857142855 x2 = -0.87189683 + -0.7857142855 Combine like terms: -0.87189683 + -0.7857142855 = -1.6576111155 x2 = -1.6576111155 Simplifying x2 = -1.6576111155 Reorder the terms: 1.6576111155 + x2 = -1.6576111155 + 1.6576111155 Combine like terms: -1.6576111155 + 1.6576111155 = 0.0000000000 1.6576111155 + 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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