Solve for f
f=2\left(x-1\right)^{2}+1
Solve for x (complex solution)
x=-\frac{\sqrt{2f-2}}{2}+1
x=\frac{\sqrt{2f-2}}{2}+1
Solve for x
x=-\frac{\sqrt{2f-2}}{2}+1
x=\frac{\sqrt{2f-2}}{2}+1\text{, }f\geq 1
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f=2\left(x^{2}-2x+1\right)+1
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
f=2x^{2}-4x+2+1
Use the distributive property to multiply 2 by x^{2}-2x+1.
f=2x^{2}-4x+3
Add 2 and 1 to get 3.
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