Question

2v^2-12 =-12v
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Answer 1

For this case we have the following equation:

`2v ^ 2-12 = -12v`

Rewriting we have:

`2v ^ 2 + 12v-12 = 0`

Dividing by 2 to both sides of the equation:

`v ^ 2 + 6v-6 = 0`

We apply the quadratic formula:

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

We have to:

`a = 1\\b = 6\\c = -6`

Substituting:

`x = \frac {-6 \pm \sqrt {6 ^ 2-4 (1) (- 6)}} {2 (1)}\\x = \frac {-6 \pm \sqrt {36 + 24}} {2}\\x = \frac {-6 \pm \sqrt {60}} {2}\\x = \frac {-6 \pm \sqrt {4 * 15}} {2}\\x = \frac {-6 \pm2 \sqrt {15}} {2}`

Thus, we have two roots:

`x_ {1} = - 3+ \sqrt {15}\\x_ {2} = - 3- \sqrt {15}`

ANswer:

`x_ {1} = - 3+ \sqrt {15}\\x_ {2} = - 3- \sqrt {15}`