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Solve for a (complex solution)
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Solve for x (complex solution)
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Solve for a
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x^{2}-ax+4=x^{2}-4x+4
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
-ax+4=x^{2}-4x+4-x^{2}
Subtract x^{2} from both sides.
-ax+4=-4x+4
Combine x^{2} and -x^{2} to get 0.
-ax=-4x+4-4
Subtract 4 from both sides.
-ax=-4x
Subtract 4 from 4 to get 0.
\left(-x\right)a=-4x
The equation is in standard form.
\frac{\left(-x\right)a}{-x}=-\frac{4x}{-x}
Divide both sides by -x.
a=-\frac{4x}{-x}
Dividing by -x undoes the multiplication by -x.
a=4
Divide -4x by -x.
x^{2}-ax+4=x^{2}-4x+4
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
x^{2}-ax+4-x^{2}=-4x+4
Subtract x^{2} from both sides.
-ax+4=-4x+4
Combine x^{2} and -x^{2} to get 0.
-ax+4+4x=4
Add 4x to both sides.
-ax+4x=4-4
Subtract 4 from both sides.
-ax+4x=0
Subtract 4 from 4 to get 0.
\left(-a+4\right)x=0
Combine all terms containing x.
\left(4-a\right)x=0
The equation is in standard form.
x=0
Divide 0 by 4-a.
x^{2}-ax+4=x^{2}-4x+4
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
-ax+4=x^{2}-4x+4-x^{2}
Subtract x^{2} from both sides.
-ax+4=-4x+4
Combine x^{2} and -x^{2} to get 0.
-ax=-4x+4-4
Subtract 4 from both sides.
-ax=-4x
Subtract 4 from 4 to get 0.
\left(-x\right)a=-4x
The equation is in standard form.
\frac{\left(-x\right)a}{-x}=-\frac{4x}{-x}
Divide both sides by -x.
a=-\frac{4x}{-x}
Dividing by -x undoes the multiplication by -x.
a=4
Divide -4x by -x.
x^{2}-ax+4=x^{2}-4x+4
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
x^{2}-ax+4-x^{2}=-4x+4
Subtract x^{2} from both sides.
-ax+4=-4x+4
Combine x^{2} and -x^{2} to get 0.
-ax+4+4x=4
Add 4x to both sides.
-ax+4x=4-4
Subtract 4 from both sides.
-ax+4x=0
Subtract 4 from 4 to get 0.
\left(-a+4\right)x=0
Combine all terms containing x.
\left(4-a\right)x=0
The equation is in standard form.
x=0
Divide 0 by 4-a.