Given
[tex](x-4)^2=5[/tex]Find
Solve the equation
Explanation
Here we use the quadratic formula to find the value of x.
first we simplify the given eqaution
[tex]\begin{gathered} (x-4)^2=5 \\ x^2+16-8x=5 \\ x^2-8x+11=0 \end{gathered}[/tex]quadratic formula is given by
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]here we have , a = 1 , b = -8 and c = 11
substitute the values in the formula ,
[tex]\begin{gathered} x=\frac{-(-8)\pm\sqrt{(-8)^2-4\times1\times11}}{2\times1} \\ \\ x=\frac{8\pm\sqrt{64-44}}{2} \\ \\ x=\frac{8\pm\sqrt{20}}{2} \\ \\ x=\frac{8\pm2\sqrt{5}}{2} \\ \\ x=4\pm\sqrt{5} \end{gathered}[/tex]Final Answer
Therefore , the correct option is D.
