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Simplifying f(x) = x2 + 6x + 8f(x + 2) Multiply f * x fx = x2 + 6x + 8f(x + 2) Reorder the terms: fx = x2 + 6x + 8f(2 + x) fx = x2 + 6x + (2 * 8f + x * 8f) fx = x2 + 6x + (16f + 8fx) Reorder the terms: fx = 16f + 8fx + 6x + x2 Solving fx = 16f + 8fx + 6x + x2 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-16f' to each side of the equation. -16f + fx = 16f + 8fx + 6x + -16f + x2 Reorder the terms: -16f + fx = 16f + -16f + 8fx + 6x + x2 Combine like terms: 16f + -16f = 0 -16f + fx = 0 + 8fx + 6x + x2 -16f + fx = 8fx + 6x + x2 Add '-8fx' to each side of the equation. -16f + fx + -8fx = 8fx + 6x + -8fx + x2 Combine like terms: fx + -8fx = -7fx -16f + -7fx = 8fx + 6x + -8fx + x2 Reorder the terms: -16f + -7fx = 8fx + -8fx + 6x + x2 Combine like terms: 8fx + -8fx = 0 -16f + -7fx = 0 + 6x + x2 -16f + -7fx = 6x + x2 Reorder the terms: -16f + -7fx + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 -16f + -7fx + -6x + -1x2 = 0 + x2 + -1x2 -16f + -7fx + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -16f + -7fx + -6x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16f + 7fx + 6x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16f + 7fx + 6x + x2)' equal to zero and attempt to solve: Simplifying 16f + 7fx + 6x + x2 = 0 Solving 16f + 7fx + 6x + x2 = 0 Move all terms containing f to the left, all other terms to the right. Add '-6x' to each side of the equation. 16f + 7fx + 6x + -6x + x2 = 0 + -6x Combine like terms: 6x + -6x = 0 16f + 7fx + 0 + x2 = 0 + -6x 16f + 7fx + x2 = 0 + -6x Remove the zero: 16f + 7fx + x2 = -6x Add '-1x2' to each side of the equation. 16f + 7fx + x2 + -1x2 = -6x + -1x2 Combine like terms: x2 + -1x2 = 0 16f + 7fx + 0 = -6x + -1x2 16f + 7fx = -6x + -1x2 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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