Answer:
Part 1) The solutions are approximately [tex]x=1.94[/tex] and [tex]x=-1.94[/tex]
Part 2) The solutions are [tex]x=-4[/tex] and [tex]x=-10[/tex]
Step-by-step explanation:
Part 1)
in this problem we have
[tex]8x^{2} +5=35[/tex]
[tex]8x^{2}=35-5[/tex]
[tex]8x^{2}=30[/tex]
[tex]x^{2}=30/8[/tex]
square root both sides
[tex]x=(+/-)\sqrt{(30/8)}\\ \\x=(+/-)1.94[/tex]
The solutions are [tex]x=1.94[/tex] and [tex]x=-1.94[/tex]
Part 2)
we know that
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]0=x^{2} +14x+40[/tex]
so
[tex]a=1\\b=14\\c=40[/tex]
substitute in the formula
[tex]x=\frac{-14(+/-)\sqrt{14^{2}-4(1)(40)}} {2(1)}[/tex]
[tex]x=\frac{-14(+/-)\sqrt{36}} {2}[/tex]
[tex]x=\frac{-14(+/-)6} {2}[/tex]
[tex]x=\frac{-14(+)6} {2}=-4[/tex]
[tex]x=\frac{-14(-)6} {2}=-10[/tex]
The solutions are [tex]x=-4[/tex] and [tex]x=-10[/tex]
