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Simplifying 16(x2 + 1) = 4(x + 4) Reorder the terms: 16(1 + x2) = 4(x + 4) (1 * 16 + x2 * 16) = 4(x + 4) (16 + 16x2) = 4(x + 4) Reorder the terms: 16 + 16x2 = 4(4 + x) 16 + 16x2 = (4 * 4 + x * 4) 16 + 16x2 = (16 + 4x) Add '-16' to each side of the equation. 16 + -16 + 16x2 = 16 + -16 + 4x Combine like terms: 16 + -16 = 0 0 + 16x2 = 16 + -16 + 4x 16x2 = 16 + -16 + 4x Combine like terms: 16 + -16 = 0 16x2 = 0 + 4x 16x2 = 4x Solving 16x2 = 4x Solving for variable 'x'. Reorder the terms: -4x + 16x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -4x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(-1 + 4x) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-1 + 4x)' equal to zero and attempt to solve: Simplifying -1 + 4x = 0 Solving -1 + 4x = 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 + 4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4x = 0 + 1 4x = 0 + 1 Combine like terms: 0 + 1 = 1 4x = 1 Divide each side by '4'. x = 0.25 Simplifying x = 0.25Solution
x = {0, 0.25}
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