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Solve for k (complex solution)
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Solve for k
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Solve for x (complex solution)
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Solve for x
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k\left(x^{2}-2x+1\right)+2=kx-k+2
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
kx^{2}-2kx+k+2=kx-k+2
Use the distributive property to multiply k by x^{2}-2x+1.
kx^{2}-2kx+k+2-kx=-k+2
Subtract kx from both sides.
kx^{2}-3kx+k+2=-k+2
Combine -2kx and -kx to get -3kx.
kx^{2}-3kx+k+2+k=2
Add k to both sides.
kx^{2}-3kx+2k+2=2
Combine k and k to get 2k.
kx^{2}-3kx+2k=2-2
Subtract 2 from both sides.
kx^{2}-3kx+2k=0
Subtract 2 from 2 to get 0.
\left(x^{2}-3x+2\right)k=0
Combine all terms containing k.
k=0
Divide 0 by x^{2}-3x+2.
k\left(x^{2}-2x+1\right)+2=kx-k+2
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
kx^{2}-2kx+k+2=kx-k+2
Use the distributive property to multiply k by x^{2}-2x+1.
kx^{2}-2kx+k+2-kx=-k+2
Subtract kx from both sides.
kx^{2}-3kx+k+2=-k+2
Combine -2kx and -kx to get -3kx.
kx^{2}-3kx+k+2+k=2
Add k to both sides.
kx^{2}-3kx+2k+2=2
Combine k and k to get 2k.
kx^{2}-3kx+2k=2-2
Subtract 2 from both sides.
kx^{2}-3kx+2k=0
Subtract 2 from 2 to get 0.
\left(x^{2}-3x+2\right)k=0
Combine all terms containing k.
k=0
Divide 0 by x^{2}-3x+2.