Question

X^2 - 5x - 13 = 0
How do I solve this

Answer 1

`{x}^(2) - 5x - 13 = 0 \\ ( {x})^(2) - 2(x)( (5)/(2) ) + ( (5)/(2))^(2) - (77)/(4) = 0 \\ {(x - (5)/(2) })^(2) - ( ( √(77) )/(2) )^(2) = 0 \\ (x - (5)/(2) - ( √(77) )/(2) )(x - (5)/(2) + ( √(77) )/(2) ) = 0 \\ (x - ((5)/(2) + ( √(77) )/(2)) )(x - ( (5)/(2) - ( √(77) )/(2) )) = 0 \\ \: x = (5)/(2) + ( √(77) )/(2) \: or \: x = (5)/(2) - ( √(77) )/(2)\\ then \: x = (5 + √(77) )/(2) \: or\: x = (5 - √(77) )/(2)`