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Simplifying 3x4 + x2 + -18 = 0 Reorder the terms: -18 + x2 + 3x4 = 0 Solving -18 + x2 + 3x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + 0.3333333333x2 + x4 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 0.3333333333x2 + 6 + x4 = 0 + 6 Reorder the terms: -6 + 6 + 0.3333333333x2 + x4 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 0.3333333333x2 + x4 = 0 + 6 0.3333333333x2 + x4 = 0 + 6 Combine like terms: 0 + 6 = 6 0.3333333333x2 + x4 = 6 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x2 + 0.25 + x4 = 6 + 0.25 Reorder the terms: 0.25 + 0.3333333333x2 + x4 = 6 + 0.25 Combine like terms: 6 + 0.25 = 6.25 0.25 + 0.3333333333x2 + x4 = 6.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x2 + 0.5) equal to 2.5 and -2.5.Subproblem 1
x2 + 0.5 = 2.5 Simplifying x2 + 0.5 = 2.5 Reorder the terms: 0.5 + x2 = 2.5 Solving 0.5 + x2 = 2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 2.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 2.5 + -0.5 x2 = 2.5 + -0.5 Combine like terms: 2.5 + -0.5 = 2 x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}Subproblem 2
x2 + 0.5 = -2.5 Simplifying x2 + 0.5 = -2.5 Reorder the terms: 0.5 + x2 = -2.5 Solving 0.5 + x2 = -2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -2.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -2.5 + -0.5 x2 = -2.5 + -0.5 Combine like terms: -2.5 + -0.5 = -3 x2 = -3 Simplifying x2 = -3 Reorder the terms: 3 + x2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + x2 = 0 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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