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Simplifying -0.2116x4 + 6.25x2 + 729 = 0 Reorder the terms: 729 + 6.25x2 + -0.2116x4 = 0 Solving 729 + 6.25x2 + -0.2116x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2116 the coefficient of the squared term: Divide each side by '-0.2116'. -3445.179584 + -29.536862x2 + x4 = 0 Move the constant term to the right: Add '3445.179584' to each side of the equation. -3445.179584 + -29.536862x2 + 3445.179584 + x4 = 0 + 3445.179584 Reorder the terms: -3445.179584 + 3445.179584 + -29.536862x2 + x4 = 0 + 3445.179584 Combine like terms: -3445.179584 + 3445.179584 = 0.000000 0.000000 + -29.536862x2 + x4 = 0 + 3445.179584 -29.536862x2 + x4 = 0 + 3445.179584 Combine like terms: 0 + 3445.179584 = 3445.179584 -29.536862x2 + x4 = 3445.179584 The x term is -29.536862x2. Take half its coefficient (-14.768431). Square it (218.1065542) and add it to both sides. Add '218.1065542' to each side of the equation. -29.536862x2 + 218.1065542 + x4 = 3445.179584 + 218.1065542 Reorder the terms: 218.1065542 + -29.536862x2 + x4 = 3445.179584 + 218.1065542 Combine like terms: 3445.179584 + 218.1065542 = 3663.2861382 218.1065542 + -29.536862x2 + x4 = 3663.2861382 Factor a perfect square on the left side: (x2 + -14.768431)(x2 + -14.768431) = 3663.2861382 Calculate the square root of the right side: 60.52508685 Break this problem into two subproblems by setting (x2 + -14.768431) equal to 60.52508685 and -60.52508685.Subproblem 1
x2 + -14.768431 = 60.52508685 Simplifying x2 + -14.768431 = 60.52508685 Reorder the terms: -14.768431 + x2 = 60.52508685 Solving -14.768431 + x2 = 60.52508685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.768431' to each side of the equation. -14.768431 + 14.768431 + x2 = 60.52508685 + 14.768431 Combine like terms: -14.768431 + 14.768431 = 0.000000 0.000000 + x2 = 60.52508685 + 14.768431 x2 = 60.52508685 + 14.768431 Combine like terms: 60.52508685 + 14.768431 = 75.29351785 x2 = 75.29351785 Simplifying x2 = 75.29351785 Take the square root of each side: x = {-8.677183751, 8.677183751}Subproblem 2
x2 + -14.768431 = -60.52508685 Simplifying x2 + -14.768431 = -60.52508685 Reorder the terms: -14.768431 + x2 = -60.52508685 Solving -14.768431 + x2 = -60.52508685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.768431' to each side of the equation. -14.768431 + 14.768431 + x2 = -60.52508685 + 14.768431 Combine like terms: -14.768431 + 14.768431 = 0.000000 0.000000 + x2 = -60.52508685 + 14.768431 x2 = -60.52508685 + 14.768431 Combine like terms: -60.52508685 + 14.768431 = -45.75665585 x2 = -45.75665585 Simplifying x2 = -45.75665585 Reorder the terms: 45.75665585 + x2 = -45.75665585 + 45.75665585 Combine like terms: -45.75665585 + 45.75665585 = 0.00000000 45.75665585 + x2 = 0.00000000 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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