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Simplifying -1f(x + h) = 3x2 + 5x + 4 Reorder the terms: -1f(h + x) = 3x2 + 5x + 4 (h * -1f + x * -1f) = 3x2 + 5x + 4 (-1fh + -1fx) = 3x2 + 5x + 4 Reorder the terms: -1fh + -1fx = 4 + 5x + 3x2 Solving -1fh + -1fx = 4 + 5x + 3x2 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Reorder the terms: -4 + -1fh + -1fx + -5x + -3x2 = 4 + 5x + 3x2 + -4 + -5x + -3x2 Reorder the terms: -4 + -1fh + -1fx + -5x + -3x2 = 4 + -4 + 5x + -5x + 3x2 + -3x2 Combine like terms: 4 + -4 = 0 -4 + -1fh + -1fx + -5x + -3x2 = 0 + 5x + -5x + 3x2 + -3x2 -4 + -1fh + -1fx + -5x + -3x2 = 5x + -5x + 3x2 + -3x2 Combine like terms: 5x + -5x = 0 -4 + -1fh + -1fx + -5x + -3x2 = 0 + 3x2 + -3x2 -4 + -1fh + -1fx + -5x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -4 + -1fh + -1fx + -5x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + fh + fx + 5x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + fh + fx + 5x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + fh + fx + 5x + 3x2 = 0 Solving 4 + fh + fx + 5x + 3x2 = 0 Move all terms containing f to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + fh + fx + 5x + -4 + 3x2 = 0 + -4 Reorder the terms: 4 + -4 + fh + fx + 5x + 3x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + fh + fx + 5x + 3x2 = 0 + -4 fh + fx + 5x + 3x2 = 0 + -4 Combine like terms: 0 + -4 = -4 fh + fx + 5x + 3x2 = -4 Add '-5x' to each side of the equation. fh + fx + 5x + -5x + 3x2 = -4 + -5x Combine like terms: 5x + -5x = 0 fh + fx + 0 + 3x2 = -4 + -5x fh + fx + 3x2 = -4 + -5x Add '-3x2' to each side of the equation. fh + fx + 3x2 + -3x2 = -4 + -5x + -3x2 Combine like terms: 3x2 + -3x2 = 0 fh + fx + 0 = -4 + -5x + -3x2 fh + fx = -4 + -5x + -3x2 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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