Question

What are the solutions of this quadratic equation x^2+8x+3=0

Answer 1

Explanation:

Given quadratic equation is:

`x^2+8x+3=0 \\ equating \: it \: with \: \\ a {x}^(2) + bx + c = 0 \: we \: find : \\ a = 1 \: \: b = 8 \: \: c = 3 \\ \\ {b}^(2) - 4ac \\ = {8}^(2) - 4 * 1 * 3 \\ = 64 - 12 \\ = 52 \\ \\ \because \: x = \frac{ - b \pm \sqrt{{b}^(2) - 4ac } }{2a} \\ \\ \therefore\: x = ( - 8 \pm √(52 ) )/(2 * 1) \\ \\ \therefore\: x = ( - 8 \pm √(4 * 13 ) )/(2 ) \\ \\ \therefore\: x = ( - 8 \pm 2√(13) )/(2 ) \\ \\ \therefore\: x = ( 2(- 4\pm √(13)) )/(2 ) \\ \\ \therefore\: x =- 4\pm √(13) \\ \\ \therefore\: x =- 4\pm3.6 \\ \\ \therefore\: x =- 4 + 3.6 \: \: or \: \: x=- 4 - 3.6 \\ \\ \therefore\: x =- 0.4 \: \: or \: \: x=- 7.6 \\ \\ \therefore\: x = \{ - 7.6, \: \: - 0.4 \}`