Answer:
The negative solution is between -3 and -2
The positive solution is between 11 and 13
Step-by-step explanation:
we have
[tex]0=x^{2} -10x-27[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2} -10x-27=0[/tex]
so
[tex]a=1\\b=-10\\c=-27[/tex]
substitute in the formula
[tex]x=\frac{10(+/-)\sqrt{-10^{2}-4(1)(-27)}} {2(1)}[/tex]
[tex]x=\frac{10(+/-)\sqrt{208}} {2}[/tex]
[tex]x=\frac{10(+)\sqrt{208}} {2}=12.21[/tex]
[tex]x=\frac{10(-)\sqrt{208}} {2}=-2.21[/tex]
therefore
The negative solution is between -3 and -2
The positive solution is between 11 and 13
