Question

I really need help on this can you help me please

Answer 1

The value of x is Option D.

`x=\frac{7\pm i\sqrt[]{3}}{2}`

EXPLANATION :

From the given problem,

`x^2-7x=-13`

First step is to rewrite the equation in the form ax^2 + bx + c = 0

`\begin{gathered} x^2-7x=-13 \\ x^2-7x+13=0 \end{gathered}`

Second step is to use the quadratic formula in finding the values of x :

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

where a, b and c are the coefficients of the quadratic equation.

a = 1, b = -7 and c = 13

`\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}`

Note that i = √-1