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Simplifying F(x) = 5x2 + 3x Multiply F * x xF = 5x2 + 3x Reorder the terms: xF = 3x + 5x2 Solving xF = 3x + 5x2 Solving for variable 'x'. Reorder the terms: -3x + xF + -5x2 = 3x + 5x2 + -3x + -5x2 Reorder the terms: -3x + xF + -5x2 = 3x + -3x + 5x2 + -5x2 Combine like terms: 3x + -3x = 0 -3x + xF + -5x2 = 0 + 5x2 + -5x2 -3x + xF + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -3x + xF + -5x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + F + -5x) = 0Subproblem 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 '(-3 + F + -5x)' equal to zero and attempt to solve: Simplifying -3 + F + -5x = 0 Solving -3 + F + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + F + 3 + -5x = 0 + 3 Reorder the terms: -3 + 3 + F + -5x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + F + -5x = 0 + 3 F + -5x = 0 + 3 Combine like terms: 0 + 3 = 3 F + -5x = 3 Add '-1F' to each side of the equation. F + -1F + -5x = 3 + -1F Combine like terms: F + -1F = 0 0 + -5x = 3 + -1F -5x = 3 + -1F Divide each side by '-5'. x = -0.6 + 0.2F Simplifying x = -0.6 + 0.2FSolution
x = {0, -0.6 + 0.2F}
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