Question

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

Answer 1

Step-by-step explanation:

Given quadratic equation is:

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