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ANSWER
[tex]x=3.732;x=0.268[/tex]EXPLANATION
We want to solve the given equation for x:
[tex]x^2-4x+1=0[/tex]To do this, apply the quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]where a = coefficient of x²
b = coefficient of x
c = constant term
From the equation, we have that:
[tex]a=1,b=-4,c=1[/tex]Therefore, solving for x:
[tex]\begin{gathered} x=\frac{-(-4)\pm\sqrt{(-4)^2-(4*1*1)}}{2(1)} \\ x=\frac{4\pm\sqrt{16-4}}{2}=\frac{4\pm\sqrt{12}}{2} \\ x=\frac{4+\sqrt{12}}{2};x=\frac{4-\sqrt{12}}{2} \\ x=\frac{4+3.464}{2};x=\frac{4-3.464}{2} \\ x=\frac{7.464}{2};x=\frac{0.536}{2} \\ x=3.732;x=0.268 \end{gathered}[/tex]That is the solution to the equation.
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