Question

Solve this quadratic equation. Return the answer in 2 decimals ?

Answer 1

`x=3.64,-0.14`

Explanation:

We have `2x-1/x=7`

Multiplying both sides by `x`, we get:

`x(2x-1/x)=7x`

`2x^2-1=7x`

`2x^2-7x-1=0`

Now we have a quadratic equation. For any `ax^2+bx+c=0`, where `a!=0,` `x=(-b+-sqrt(b^2-4ac))/(2a)`.

Here, `a=2,b=-7,c=-1`

We can input:

`(-(-7)+-sqrt((-7)^2-4*2*-1))/(2*2)`

`(7+-sqrt(49+8))/4`

`(7+-sqrt(57))/4`

`x=(7+sqrt(57))/4,(7-sqrt(57))/4`

`x=3.64,-0.14`

Answer 2

`x = 3.64 or x = -0.14`

Explanation:

This is clearly not a comfortable form to work with.
Multiply through by `x` and re-arrange the equation into the form:

`ax^2 +bx+c=0`

`2xcolor(blue)(xx x) -1/xcolor(blue)(xx x) =7color(blue)(xx x)`

`2x^2 -1=7x`

`2x^2 -7x-1=0" "larr` it does not factorise

`x= (-b+-sqrt(b^2-4ac))/(2a)`

`x = (-(-7)+-sqrt((-7)^2 -4(2)(-1)))/(2(2))`

`x = (7+-sqrt(49+8))/(4)`

`x = (7+sqrt57)/4 = 3.64`

`x = (7-sqrt57)/4 = -0.14`

Answer 3

See below...

Explanation:

First we need the standard format of `ax^2+bx+c=0`

First we multiply all by `x` to remove the fraction.

`2x-1/x=7 => 2x^2-1=7x`

Now we move the `7x` over by subtracting both sides by `7x`

`2x^2-1=7x => 2x^2-7x-1=0`

As we want the answers to `2d.p` it strongly hints that we need to use the quadratic formula.

We know that `x=-b+-sqrt(b^2-4ac)/(2a)`

Now from our equation we know that ...

`a =2`, `b=-7` and `c=-1`

Now we plug these into our formula, but as we have a `+` and a `-` we have to do it twice.

`x=-(-7)+sqrt((-7)^2-4(2)(-1))/(2(2))`
`x=-(-7)-sqrt((-7)^2-4(2)(-1))/(2(2))`

Now we put each one into our calculator and round to `2d.p.`

`therefore x =-0.14 , x =3.64`

Both to `2d.p`