Question

Solve 5x2-2x-8=0 using the quadratic formula.

Answer 1

`x=(1+√(41))/(5),\\x=(1-√(41))/(5)`

Explanation:

The quadratic formula states that the solutions for a quadratic is standard form
`ax^2+bx+c` are equal to
`x=(-b\pm √(b^2-4ac))/(2a)`.

In
`5x^2-2x-8=0`, we can assign the values:

• 
  `a` of 5
• 
  `b` of -2
• 
  `c` of -8

Thus, we have:

`x=(-(-2)\pm √((-2)^2-4(5)(-8)))/(2(5)),\\x=(2\pm √(164))/(10),\\\begin{cases}x=(2+ √(164))/(10), x=(1)/(5)+(√(41))/(5)=(1+√(41))/(5)\\x=(2- √(164))/(10), x=(1)/(5)-(√(41))/(5)=(1-√(41))/(5)\end{cases}`

Answer 2

(1+√41)/5, (1-√41)/5

Explanation:

quadratic formula is (-b±√(b^2-4ac))/2a

in this equation,

a = 5

b = -2

c = -8

plug in the values

(2±√(4 - 4(5)(-8))/10

(2±√(4 + 160)/10

(2±√(164)/10

(2±2√(41))/10

1. (2+2√41)/10

(1+√41)/5

2. (2-2√41)/10

(1-√41)/5