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Simplifying 8 = 0.5x4 + 3x2 Reorder the terms: 8 = 3x2 + 0.5x4 Solving 8 = 3x2 + 0.5x4 Solving for variable 'x'. Reorder the terms: 8 + -3x2 + -0.5x4 = 3x2 + -3x2 + 0.5x4 + -0.5x4 Combine like terms: 3x2 + -3x2 = 0 8 + -3x2 + -0.5x4 = 0 + 0.5x4 + -0.5x4 8 + -3x2 + -0.5x4 = 0.5x4 + -0.5x4 Combine like terms: 0.5x4 + -0.5x4 = 0.0 8 + -3x2 + -0.5x4 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -16 + 6x2 + x4 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 6x2 + 16 + x4 = 0 + 16 Reorder the terms: -16 + 16 + 6x2 + x4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 6x2 + x4 = 0 + 16 6x2 + x4 = 0 + 16 Combine like terms: 0 + 16 = 16 6x2 + x4 = 16 The x term is 6x2. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x2 + 9 + x4 = 16 + 9 Reorder the terms: 9 + 6x2 + x4 = 16 + 9 Combine like terms: 16 + 9 = 25 9 + 6x2 + x4 = 25 Factor a perfect square on the left side: (x2 + 3)(x2 + 3) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (x2 + 3) equal to 5 and -5.Subproblem 1
x2 + 3 = 5 Simplifying x2 + 3 = 5 Reorder the terms: 3 + x2 = 5 Solving 3 + x2 = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x2 = 5 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = 5 + -3 x2 = 5 + -3 Combine like terms: 5 + -3 = 2 x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}Subproblem 2
x2 + 3 = -5 Simplifying x2 + 3 = -5 Reorder the terms: 3 + x2 = -5 Solving 3 + x2 = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x2 = -5 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = -5 + -3 x2 = -5 + -3 Combine like terms: -5 + -3 = -8 x2 = -8 Simplifying x2 = -8 Reorder the terms: 8 + x2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + 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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