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Simplifying (6x4) + (48x2) = 32 Reorder the terms: (48x2) + (6x4) = 32 Solving (48x2) + (6x4) = 32 Solving for variable 'x'. Reorder the terms: -32 + (48x2) + (6x4) = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + (48x2) + (6x4) = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + (24x2) + (3x4)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + (24x2) + (3x4))' equal to zero and attempt to solve: Simplifying -16 + (24x2) + (3x4) = 0 Solving -16 + (24x2) + (3x4) = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + (8x2) + x4 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + (8x2) + 5.333333333 + x4 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + (8x2) + x4 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + (8x2) + x4 = 0 + 5.333333333 (8x2) + x4 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 (8x2) + x4 = 5.333333333 The x term is (8x2). Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. (8x2) + 16 + x4 = 5.333333333 + 16 Reorder the terms: 16 + (8x2) + x4 = 5.333333333 + 16 Combine like terms: 5.333333333 + 16 = 21.333333333 16 + (8x2) + x4 = 21.333333333 Factor a perfect square on the left side: ((x2) + 4)((x2) + 4) = 21.333333333 Calculate the square root of the right side: 4.618802153 Break this problem into two subproblems by setting ((x2) + 4) equal to 4.618802153 and -4.618802153.Subproblem 1
(x2) + 4 = 4.618802153 Simplifying (x2) + 4 = 4.618802153 x2 + 4 = 4.618802153 Reorder the terms: 4 + x2 = 4.618802153 Solving 4 + x2 = 4.618802153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = 4.618802153 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 4.618802153 + -4 x2 = 4.618802153 + -4 Combine like terms: 4.618802153 + -4 = 0.618802153 x2 = 0.618802153 Simplifying x2 = 0.618802153 Take the square root of each side: x = {-0.786639786, 0.786639786}Subproblem 2
(x2) + 4 = -4.618802153 Simplifying (x2) + 4 = -4.618802153 x2 + 4 = -4.618802153 Reorder the terms: 4 + x2 = -4.618802153 Solving 4 + x2 = -4.618802153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = -4.618802153 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -4.618802153 + -4 x2 = -4.618802153 + -4 Combine like terms: -4.618802153 + -4 = -8.618802153 x2 = -8.618802153 Simplifying x2 = -8.618802153 Reorder the terms: 8.618802153 + x2 = -8.618802153 + 8.618802153 Combine like terms: -8.618802153 + 8.618802153 = 0.000000000 8.618802153 + 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. 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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