Question

Solve the equation using the quadratic formula. Enter each solution in simplest form.

x^2-4x+23=0

Answer 1

For this case we have the following quadratic equation:

`x ^ 2-4x + 23 = 0`

The solutions will be given by:

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

Where:

`a = 1\\b = -4\\c = 23`

Substituting the values we have:

`x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (1) (23)}} {2 (1)}\\x = \frac {4 \pm \sqrt {16-92}} {2}\\x = \frac {4 \pm \sqrt {-76}} {2}\\x = \frac {4 \pm \sqrt {76i ^ 2}} {2}\\x = \frac {4 \pmi \sqrt {76}} {2}\\x = \frac {4 \pmi \sqrt {2 ^ 2 * 19}} {2}\\x = \frac {4 \pm2i \sqrt {19}} {2}\\x = 2 \pm i\sqrt {19}`

We have two roots:

`x_ {1} = 2-i \sqrt {19}\\x_ {2} = 2 + i \sqrt {19}`

ANswer:

`x_ {1} = 2-i\sqrt {19}\\x_ {2} = 2 + i\sqrt {19}`