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Simplifying (2x2 + 3)(2x2 + 3) = 4x(x3 + 6) Reorder the terms: (3 + 2x2)(2x2 + 3) = 4x(x3 + 6) Reorder the terms: (3 + 2x2)(3 + 2x2) = 4x(x3 + 6) Multiply (3 + 2x2) * (3 + 2x2) (3(3 + 2x2) + 2x2 * (3 + 2x2)) = 4x(x3 + 6) ((3 * 3 + 2x2 * 3) + 2x2 * (3 + 2x2)) = 4x(x3 + 6) ((9 + 6x2) + 2x2 * (3 + 2x2)) = 4x(x3 + 6) (9 + 6x2 + (3 * 2x2 + 2x2 * 2x2)) = 4x(x3 + 6) (9 + 6x2 + (6x2 + 4x4)) = 4x(x3 + 6) Combine like terms: 6x2 + 6x2 = 12x2 (9 + 12x2 + 4x4) = 4x(x3 + 6) Reorder the terms: 9 + 12x2 + 4x4 = 4x(6 + x3) 9 + 12x2 + 4x4 = (6 * 4x + x3 * 4x) 9 + 12x2 + 4x4 = (24x + 4x4) Add '-4x4' to each side of the equation. 9 + 12x2 + 4x4 + -4x4 = 24x + 4x4 + -4x4 Combine like terms: 4x4 + -4x4 = 0 9 + 12x2 + 0 = 24x + 4x4 + -4x4 9 + 12x2 = 24x + 4x4 + -4x4 Combine like terms: 4x4 + -4x4 = 0 9 + 12x2 = 24x + 0 9 + 12x2 = 24x Solving 9 + 12x2 = 24x Solving for variable 'x'. Reorder the terms: 9 + -24x + 12x2 = 24x + -24x Combine like terms: 24x + -24x = 0 9 + -24x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -8x + 4x2) = 0 Factor a trinomial. 3((1 + -2x)(3 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {0.5, 1.5}
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