[tex]Solution, \mathrm{Isolate}\:x\:\mathrm{for}\:If\left(I,\:x\right)Q\left(x\right)=4x^2-1:\quad x=\frac{\sqrt{f\left(I,\:x\right)Q\left(x\right)I+1}}{2},\:x=-\frac{\sqrt{f\left(I,\:x\right)Q\left(x\right)I+1}}{2}[/tex]
[tex]Steps: If\left(I,\:x\right)Q\left(x\right)=4x^2-1[/tex]
[tex]\mathrm{Switch\:sides}, 4x^2-1=If\left(I,\:x\right)Q\left(x\right)[/tex]
[tex]\mathrm{Add\:}1\mathrm{\:to\:both\:sides}, 4x^2-1+1=If\left(I,\:x\right)Q\left(x\right)+1[/tex]
[tex]\mathrm{Simplify}, 4x^2=If\left(I,\:x\right)Q\left(x\right)+1[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}4, \frac{4x^2}{4}=\frac{If\left(I,\:x\right)Q\left(x\right)}{4}+\frac{1}{4}[/tex]
[tex]\mathrm{Simplify}, x^2=\frac{f\left(I,\:x\right)Q\left(x\right)I+1}{4}[/tex]
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}, x=\sqrt{\frac{f\left(I,\:x\right)Q\left(x\right)I+1}{4}},\:x=-\sqrt{\frac{f\left(I,\:x\right)Q\left(x\right)I+1}{4}},\sqrt{\frac{f\left(I,\:x\right)Q\left(x\right)I+1}{4}}=\frac{\sqrt{f\left(I,\:x\right)Q\left(x\right)I+1}}{2},-\sqrt{\frac{f\left(I,\:x\right)Q\left(x\right)I+1}{4}}=-\frac{\sqrt{f\left(I,\:x\right)Q\left(x\right)I+1}}{2}[/tex]
The correct answer is [tex]x=\frac{\sqrt{f\left(I,\:x\right)Q\left(x\right)I+1}}{2},\:x=-\frac{\sqrt{f\left(I,\:x\right)Q\left(x\right)I+1}}{2}[/tex]
