Question

Find the exact roots of x²-2x-10=4x​

Answer 1

`x = 3 - √(19) \: \: or \: \: x = 3 + √(19)`

Explanation:

The given equation is

`{x}^(2) - 2x - 10 = 4x`

We group the linear terms to get:

`{x}^(2) - 2x - 4x - 10 = 0`

`{x}^(2) - 6x - 10 = 0`

We compare to

`a {x}^(2) + bx + c = 0`

This means

a=1, b=-6 and c=-10

We plug in the values into the quadratic formula:

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

This gives us

`x = \frac{ - -6 \pm \sqrt{ {( - 6)}^(2) - 4 * 1 * - 10 } }{2 * 1}`

`x = ( 6 \pm √( 36 + 40 ) )/(2)`

`x = ( 6 \pm √(76 ) )/(2)`

`x = ( - 6 \pm 2√(19) )/(2)`

`x = 3 \pm √(19)`

The solutions are

`x =3 + √(19)`

or

`x = 3 - √(19)`