ANSWER :
The value of x is Option D.
[tex]x=\frac{7\pm i\sqrt[]{3}}{2}[/tex]
EXPLANATION :
From the given problem,
[tex]x^2-7x=-13[/tex]
First step is to rewrite the equation in the form ax^2 + bx + c = 0
[tex]\begin{gathered} x^2-7x=-13 \\ x^2-7x+13=0 \end{gathered}[/tex]
Second step is to use the quadratic formula in finding the values of x :
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
where a, b and c are the coefficients of the quadratic equation.
a = 1, b = -7 and c = 13
[tex]\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4(1)(13)}}{2(1)} \\ x=\frac{7\pm\sqrt[]{49-52}}{2} \\ x=\frac{7\pm\sqrt[]{-3}}{2} \\ x=\frac{7\pm i\sqrt[]{3}}{2} \end{gathered}[/tex]
Note that i = √-1
