Question

Solve using quadratic formula x^2+8x=7

Answer 1

For this case we have the following quadratic equation:

`x ^ 2 + 8x = 7\\x ^ 2 + 8x-7 = 0`

Where:

`a = 1\\b = 8\\c = -7`

We find the solution by:

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

Substituting the values we have:

`x = \frac {-8 \pm \sqrt {8 ^ 2-4 (1) (- 7)}} {2 (1)}\\x = \frac {-8 \pm \sqrt {64 + 28}} {2}\\x = \frac {-8 \pm \sqrt {92}} {2}\\x = \frac {-8 \pm \sqrt {2 ^ 2 * 23}} {2}\\x = \frac {-8 \pm2 \sqrt {23}} {2}\\x = -4 \pm \sqrt {23}`

Thus, we have two roots:

`x_ {1} = - 4+ \sqrt {23}\\x_ {2} = - 4- \sqrt {23}`

Answer:

`x_ {1} = - 4+ \sqrt {23}\\x_ {2} = - 4- \sqrt {23}`