Question

Solve the quadratic equation. Show all of your steps. x 2 + 3 x − 5 = 0

Answer 1

For this case we have the following quadratic equation:

$x ^ 2 + 3x-5 = 0$

Where:

$a = 1\\b = 3\\c = -5$

We look for the solution using the following formula:

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

Substituting the values:

$x = \frac {-3 \pm \sqrt {3 ^ 2-4 (1) (- 5)}} {2 (1)}\\x = \frac {-3 \pm \sqrt {9 + 20}} {2}\\x = \frac {-3 \pm \sqrt {29}} {2}$

Thus, we have two roots:

$x_ {1} = \frac {-3+ \sqrt {29}} {2}\\x_ {2} = \frac {-3- \sqrt {29}} {2}$

Answer:

$x_ {1} = \frac {-3+ \sqrt {29}} {2}\\x_ {2} = \frac {-3- \sqrt {29}} {2}$