Question

1. Solve.

x^2+9x+2=0

Enter your answers, as exact values, in the boxes.

Answer 1

`x=(-9)/(2) +(1)/(2) √(73)` or
`x=(-9)/(2) +(-1)/(2) √(73)`

Explanation:

Step 1: Use quadratic formula with a=1, b=9, c=2.

`x=\frac{-b±\sqrt{b^(2) -4ac} }{2a}`

`x=\frac{-(9)±\sqrt{(9)^(2)-4(1)(2)} }{2(1)}`

`x=(-9±√(73) )/(2)`

`x=(-9)/(2) +(1)/(2) √(73)` or
`x=(-9)/(2) +(-1)/(2) √(73)`

(Ignore the Â)

Answer 2

The exact values of x is 0 or -8.

Explanation:

Given : Quadratic equation
`x^2+9x+2=0`

To find : Solve the equation ?

Solution :

Applying quadratic formula of quadratic equation
`ax^2+bx+c=0` is
`x=(-b\pm√(b^2-4ac))/(2a)`

Here, a=1, b=9 and c=2

Substitute the value,

`x=(-9\pm√(9^2-4(1)(2)))/(2(1))`

`x=(-9\pm√(81-8))/(2)`

`x=(-9\pm√(73))/(2)`

`x=(-9+√(73))/(2),(-9-√(73))/(2)`

`x=-0.22,-8.77`

Therefore, the exact values of x is 0 or -8.