Question

Solve the quadratic equation using square roots method.Leave the answer in irrational form. 15-6x-2x^2=0 HELP

Answer 1

The answer is

`x_1 = ( - 3 + √(39) )/(2) \: \:, \: \: \: \: x _2 = ( - 3 - √(39) )/(2) \\`

Explanation:

15 - 6x - 2x² = 0

Rewriting it we have

2x² + 6x - 15 = 0

Using the quadratic formula that's

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

From the question

a = 2 , b = 6 , c = - 15

So we have

`x = \frac{ - 6 \pm \sqrt{ {6}^(2) - 4(2)( - 15) } }{2(2)} \\ = ( - 6\pm √(36 + 120) )/(4) \\ = ( - 6\pm √(156) )/(4) \: \: \: \: \: \: \: \: \: \: \\ = ( - 6\pm2 √(39) )/(4) \: \: \: \: \: \: \: \: \: \\ = - (6)/(4) \pm (2 √(39) )/(4) \: \: \: \: \: \: \: \: \\ = - (3)/(2) \pm ( √(39) )/(2) \: \: \: \: \: \: \: \: \: \: \\ = ( - 3\pm √(39) )/(2) \: \: \: \: \: \: \: \: \: \: \:`

Separate the solutions

We have the final answer as

`x_1 = ( - 3 + √(39) )/(2) \: \: \: \: \: \: x _2 = ( - 3 - √(39) )/(2) \\`

Hope this helps you