Question

Solve for xtle=" \bold{x^{2} + 6x + 5 = 0}" alt=" \bold{x^{2} + 6x + 5 = 0}" align="absmiddle" class="latex-formula">

ty! ~

Answer 1

Answer:

x²+6x+5=0

On comparing with the equation

ax² + bx + c = 0

a=1, b = 6 and c = 5

Now

b²– 4ac = 6² – 4 x 1 x 5 = 36 - 20 = 16

$x = \frac{ - b \:± \: \sqrt{b {}^{2} - 4ac } }{2a} \\ \\ x = \frac{ - 6\:± \: \sqrt{16 } }{2 \times 1} \\ \\ x = \frac{ - 6± {4} }{2} \\ \\ x = \frac{ - 6 + {4} }{2} \: \: or \: \: x = \frac{ - 6 - {4} }{2} \\ \\ \implies \: x = \frac{ \cancel-2 }{ \cancel2}^{-1 }\: \: or \: \: x = \frac{ \cancel-10 }{ \cancel2}^{-5}\\ \\ \implies \: { \blue{\fbox{ \: x = - 1 \: \: \: or \: \: \:x = - 5}}}$

Answer 2

${x}^{2} + 6x + 5 = 0 \\ \\ {x}^{2} + 5x + x + 5 = 0 \\ \\ x(x + 5) + 1(x + 5) = 0 \\ \\ (x + 1)(x + 5) = 0.$

$x = - 1 \\ x = - 5.$