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Simplifying F(x) = x2 + 7x Multiply F * x xF = x2 + 7x Reorder the terms: xF = 7x + x2 Solving xF = 7x + x2 Solving for variable 'x'. Reorder the terms: -7x + xF + -1x2 = 7x + x2 + -7x + -1x2 Reorder the terms: -7x + xF + -1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 -7x + xF + -1x2 = 0 + x2 + -1x2 -7x + xF + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -7x + xF + -1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + F + -1x) = 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 '(-7 + F + -1x)' equal to zero and attempt to solve: Simplifying -7 + F + -1x = 0 Solving -7 + F + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + F + 7 + -1x = 0 + 7 Reorder the terms: -7 + 7 + F + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + F + -1x = 0 + 7 F + -1x = 0 + 7 Combine like terms: 0 + 7 = 7 F + -1x = 7 Add '-1F' to each side of the equation. F + -1F + -1x = 7 + -1F Combine like terms: F + -1F = 0 0 + -1x = 7 + -1F -1x = 7 + -1F Divide each side by '-1'. x = -7 + F Simplifying x = -7 + FSolution
x = {0, -7 + F}
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