Greetings!
Solve for a:
[tex]-8=a(2+5)^2+41[/tex]
Distribute the Parenthesis:
[tex]-8=(2a+5a)^2+41[/tex]
Apply the Exponent:
[tex]-8=(2a+5a)(2a+5a)+41[/tex]
Use Binomial Multiplication:
[tex]-8=2a(2a+5a)+5a(2a+5a)+41[/tex]
[tex]-8=(4a^2+10a^2)+(10a^2+25a^2)+41[/tex]
Combine Like Terms:
[tex]-8=4a^2+10a^2+10a^2+25a^2+41[/tex]
[tex]-8=49a^2+41[/tex]
Add -41 to both sides:
[tex](-8)+(-41)=(49a^2+41)+(-41)[/tex]
[tex]-49=49a^2[/tex]
Divide both sides by 49:
[tex] \frac{-49}{49}= \frac{49a^2}{49} [/tex]
[tex]-1=a^2[/tex]
Sqaure Root both sides:
[tex] \sqrt{-1}= \sqrt{a^2} [/tex]
[tex]-1=a[/tex]
[tex]a=-1[/tex]
The Answer Is:
[tex]\boxed{a=-1}[/tex]
I hope this helped!
-Benjamin
