Question

Solve using the quadratic formula 2x^2+8x-5=0

Answer 1

Explanation:

Hey there!!

Given,

`{x}^(2) + 8x - 5 = 0`

Comparing it with ax^2+bx+c =0 we get,

a= 1, b= 8, c= -5.

Using formula,

`x = \frac{ - b + - \sqrt{ {b}^(2) - 4ac } }{2a}`

Keep all values,

`x = \frac{ - 8 + - \sqrt{ {8}^(2) - 4 * 1 * ( - 5)} }{2 * 1}`

`x = ( - 8 + - √(64 + 20) )/(2)`

`x = ( - 8 + - √(84) )/(2)`

`x = ( - 8 + - 2 √(21) )/(2)`

Taking negative,

`x = ( - 8 - 2 √(21) )/(2)`

`x = ( - 2(4 + √(21)) )/(2)`

`x = 4 + √(21)`

Similarly, taking positive,

`x = ( - 8 + 2 √(21) )/(2)`

`x = ( - 2(4 - √(21) ) )/(2)`

`x = 4 - √(21)`

Therefore, x= (4 + root 21, 4 - root 21).

Hope it helps.....