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Simplifying 9x4 + -279x2 + -2396 = 0 Reorder the terms: -2396 + -279x2 + 9x4 = 0 Solving -2396 + -279x2 + 9x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -266.2222222 + -31x2 + x4 = 0 Move the constant term to the right: Add '266.2222222' to each side of the equation. -266.2222222 + -31x2 + 266.2222222 + x4 = 0 + 266.2222222 Reorder the terms: -266.2222222 + 266.2222222 + -31x2 + x4 = 0 + 266.2222222 Combine like terms: -266.2222222 + 266.2222222 = 0.0000000 0.0000000 + -31x2 + x4 = 0 + 266.2222222 -31x2 + x4 = 0 + 266.2222222 Combine like terms: 0 + 266.2222222 = 266.2222222 -31x2 + x4 = 266.2222222 The x term is -31x2. Take half its coefficient (-15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. -31x2 + 240.25 + x4 = 266.2222222 + 240.25 Reorder the terms: 240.25 + -31x2 + x4 = 266.2222222 + 240.25 Combine like terms: 266.2222222 + 240.25 = 506.4722222 240.25 + -31x2 + x4 = 506.4722222 Factor a perfect square on the left side: (x2 + -15.5)(x2 + -15.5) = 506.4722222 Calculate the square root of the right side: 22.504937729 Break this problem into two subproblems by setting (x2 + -15.5) equal to 22.504937729 and -22.504937729.Subproblem 1
x2 + -15.5 = 22.504937729 Simplifying x2 + -15.5 = 22.504937729 Reorder the terms: -15.5 + x2 = 22.504937729 Solving -15.5 + x2 = 22.504937729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x2 = 22.504937729 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x2 = 22.504937729 + 15.5 x2 = 22.504937729 + 15.5 Combine like terms: 22.504937729 + 15.5 = 38.004937729 x2 = 38.004937729 Simplifying x2 = 38.004937729 Take the square root of each side: x = {-6.164814493, 6.164814493}Subproblem 2
x2 + -15.5 = -22.504937729 Simplifying x2 + -15.5 = -22.504937729 Reorder the terms: -15.5 + x2 = -22.504937729 Solving -15.5 + x2 = -22.504937729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x2 = -22.504937729 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x2 = -22.504937729 + 15.5 x2 = -22.504937729 + 15.5 Combine like terms: -22.504937729 + 15.5 = -7.004937729 x2 = -7.004937729 Simplifying x2 = -7.004937729 Reorder the terms: 7.004937729 + x2 = -7.004937729 + 7.004937729 Combine like terms: -7.004937729 + 7.004937729 = 0.000000000 7.004937729 + 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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