Question

Solve for a -8=a(2+5)^2+41

Answer 1

Greetings!

Solve for a:

`-8=a(2+5)^2+41`

Distribute the Parenthesis:

`-8=(2a+5a)^2+41`

Apply the Exponent:

`-8=(2a+5a)(2a+5a)+41`

Use Binomial Multiplication:

`-8=2a(2a+5a)+5a(2a+5a)+41`


`-8=(4a^2+10a^2)+(10a^2+25a^2)+41`

Combine Like Terms:

`-8=4a^2+10a^2+10a^2+25a^2+41`


`-8=49a^2+41`

Add -41 to both sides:

`(-8)+(-41)=(49a^2+41)+(-41)`


`-49=49a^2`

Divide both sides by 49:

`(-49)/(49)= (49a^2)/(49)`


`-1=a^2`

Sqaure Root both sides:

`√(-1)= √(a^2)`


`-1=a`


`a=-1`

The Answer Is:

`\boxed{a=-1}`

I hope this helped!
-Benjamin