Answer:
a) [tex]2x^2+x-33=0[/tex]
b) [tex]x=3.8[/tex]
Step-by-step explanation:
We multiply the binomials
[tex](2x+3)(x-1)[/tex]
[tex]2x^2-2x+3x-3[/tex]
Simplify
[tex]2x^2+x-3[/tex]
Now we can set this equal to 30 since the area is 30
[tex]2x^2+x-3=30[/tex]
If. you notice in the a portion they want you to have the equation equal 0 so we subtract 30 on bot sides
[tex]2x^2+x-33=0[/tex]
We answered the A portion so now to find x we use the quadratic formula
[tex]\frac{-b+/-\sqrt{b^2-4(a)(c)} }{2a}[/tex]
Now enter what we know (we will do plus sign first
[tex]\frac{-1+\sqrt{1^2-4(2)(-33)} }{2(2)}[/tex]
Simplify
[tex]\frac{-1+\sqrt{1+264} }{4}[/tex]
[tex]\frac{-1+\sqrt{265} }{4} \\\\\frac{-1+16.2788}{4}[/tex]
[tex]3.8[/tex]
Now we do the subtract
[tex]\frac{-1-16.2788}{4}[/tex]
[tex]-4.3[/tex]
Since a side can't be negative 3.8 is the answer
I hope this helps
