Rewrite the equation by completing the square g(x) = x^2 - x - 6

g(x)=x2−x−6g(x)=x2-x-6

Set x2−x−6x2-x-6 equal to 00.

x2−x−6=0x2-x-6=0

Solve for xx.

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Factor x2−x−6x2-x-6 using the AC method.

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(x−3)(x+2)=0(x-3)(x+2)=0

If any individual factor on the left side of the equation is equal to 00, the entire expression will be equal to 00.

x−3=0x-3=0

x+2=0x+2=0

Set x−3x-3 equal to 00 and solve for xx.

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x=3x=3

Set x+2x+2 equal to 00 and solve for xx.

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x=−2x=-2

The final solution is all the values that make (x−3)(x+2)=0(x-3)(x+2)=0 true.

x=3,−2

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