Question

Find the exact roots of x²-2x-10=4x​

Answer 1

Answer:

$x = 3 - \sqrt{19} \: \: or \: \: x = 3 + \sqrt{19}$

Step-by-step 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

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

$x = \frac{ 6 \pm \sqrt{ 36 + 40 } }{2}$

$x = \frac{ 6 \pm \sqrt{76 } }{2}$

$x = \frac{ - 6 \pm 2\sqrt{19} }{2}$

$x = 3 \pm \sqrt{19}$

The solutions are

$x =3 + \sqrt{19}$

or

$x = 3 - \sqrt{19}$