Question

What are the exact solutions of x2 - 3x - 5 = 0? x = the quantity of negative 3 plus or minus the square root of 29 all over 2 x = the quantity of 3 plus or minus the square root of 29 all over 2 x = the quantity of 3 plus or minus the square root of 11 all over 2 x = the quantity of negative 3 plus or minus the square root of 11 all over 2

Answer 1

Answer:

$x= \frac{3+-\sqrt{29}}{2}$

Step-by-step explanation:

x^2 - 3 x -5=0

To solve for x we apply quadratic formula

$x= \frac{-b+-\sqrt{b^2-4ac}}{2a}$

From the given equation

a=1 , b=-3  and c=-5

Plug in all the values in the formula

$x= \frac{3+-\sqrt{(-3)^2-4(1)(-5)}}{2(1)}$

$x= \frac{3+-\sqrt{29}}{2}$

We cannot simplify square root (29)

So we keep as it is

$x= \frac{3+-\sqrt{29}}{2}$

Answer 2

$x^{2}-3x-5=0 \\ \\ \Delta=(-3)^{2}-4*1*(-5)=9+20=29 \\ \\ \sqrt{\Delta} = \sqrt{29} \\ \\ x_{1}= \frac{3- \sqrt{29} }{2} \\ \\ x_{2}= \frac{3+ \sqrt{29} }{2}$

\\\ Ben