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Simplifying f(x) = -10x2f(x + h) + -1f(x) Multiply f * x fx = -10x2f(x + h) + -1f(x) Reorder the terms: fx = -10fx2(h + x) + -1f(x) fx = (h * -10fx2 + x * -10fx2) + -1f(x) fx = (-10fhx2 + -10fx3) + -1f(x) Multiply f * x fx = -10fhx2 + -10fx3 + -1fx Reorder the terms: fx = -10fhx2 + -1fx + -10fx3 Solving fx = -10fhx2 + -1fx + -10fx3 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '10fhx2' to each side of the equation. 10fhx2 + fx = -10fhx2 + -1fx + 10fhx2 + -10fx3 Reorder the terms: 10fhx2 + fx = -10fhx2 + 10fhx2 + -1fx + -10fx3 Combine like terms: -10fhx2 + 10fhx2 = 0 10fhx2 + fx = 0 + -1fx + -10fx3 10fhx2 + fx = -1fx + -10fx3 Add 'fx' to each side of the equation. 10fhx2 + fx + fx = -1fx + fx + -10fx3 Combine like terms: fx + fx = 2fx 10fhx2 + 2fx = -1fx + fx + -10fx3 Combine like terms: -1fx + fx = 0 10fhx2 + 2fx = 0 + -10fx3 10fhx2 + 2fx = -10fx3 Add '10fx3' to each side of the equation. 10fhx2 + 2fx + 10fx3 = -10fx3 + 10fx3 Combine like terms: -10fx3 + 10fx3 = 0 10fhx2 + 2fx + 10fx3 = 0 Factor out the Greatest Common Factor (GCF), '2fx'. 2fx(5hx + 1 + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'fx' equal to zero and attempt to solve: Simplifying fx = 0 Solving fx = 0 Move all terms containing f to the left, all other terms to the right. Simplifying fx = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(5hx + 1 + 5x2)' equal to zero and attempt to solve: Simplifying 5hx + 1 + 5x2 = 0 Reorder the terms: 1 + 5hx + 5x2 = 0 Solving 1 + 5hx + 5x2 = 0 Move all terms containing f to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 5hx + -1 + 5x2 = 0 + -1 Reorder the terms: 1 + -1 + 5hx + 5x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5hx + 5x2 = 0 + -1 5hx + 5x2 = 0 + -1 Combine like terms: 0 + -1 = -1 5hx + 5x2 = -1 Add '-5hx' to each side of the equation. 5hx + -5hx + 5x2 = -1 + -5hx Combine like terms: 5hx + -5hx = 0 0 + 5x2 = -1 + -5hx 5x2 = -1 + -5hx Add '-5x2' to each side of the equation. 5x2 + -5x2 = -1 + -5hx + -5x2 Combine like terms: 5x2 + -5x2 = 0 0 = -1 + -5hx + -5x2 Simplifying 0 = -1 + -5hx + -5x2 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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