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Simplifying F(x) = 5x2 + -10x Multiply F * x xF = 5x2 + -10x Reorder the terms: xF = -10x + 5x2 Solving xF = -10x + 5x2 Solving for variable 'x'. Reorder the terms: 10x + xF + -5x2 = -10x + 5x2 + 10x + -5x2 Reorder the terms: 10x + xF + -5x2 = -10x + 10x + 5x2 + -5x2 Combine like terms: -10x + 10x = 0 10x + xF + -5x2 = 0 + 5x2 + -5x2 10x + xF + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 10x + xF + -5x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(10 + 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 '(10 + F + -5x)' equal to zero and attempt to solve: Simplifying 10 + F + -5x = 0 Solving 10 + F + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + F + -10 + -5x = 0 + -10 Reorder the terms: 10 + -10 + F + -5x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + F + -5x = 0 + -10 F + -5x = 0 + -10 Combine like terms: 0 + -10 = -10 F + -5x = -10 Add '-1F' to each side of the equation. F + -1F + -5x = -10 + -1F Combine like terms: F + -1F = 0 0 + -5x = -10 + -1F -5x = -10 + -1F Divide each side by '-5'. x = 2 + 0.2F Simplifying x = 2 + 0.2FSolution
x = {0, 2 + 0.2F}
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