Answer:
Step-by-step explanation:
x²+x-24=0
x²+x+1/4-1/4=24
x^2+x+1/4=1/4+24
[tex](x+\frac{1}{2})^2=\frac{1}{4}+24=\frac{1+96}{4}=(\frac{\sqrt{97} }{2})^2\\x+\frac{1}{2} =\pm \frac{\sqrt{97} }{2} \\either ~x+\frac{1}{2}=\frac{\sqrt{97} }{2} \\so~x+\frac{1-\sqrt{97}}{2}=0\\ or~x+\frac{1}{2} =-\frac{\sqrt{97} }{2} \\or~x+\frac{1+\sqrt{97}}{2}=0\\ Hence~ x^2-x-24=(x+\frac{1+\sqrt{97} }{2})(x+\frac{1-\sqrt{97} }{2})[/tex]
