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}`