Maximum value of an expression by equation

Question

Let $a,b \in \mathbb{R}$

Given,

$$a+b = a^2+b^2 $$

then what is the maximum value of $(a + 7b)$ ?

No idea how to deal with this.

Answer 1

Hint:

Let $a+7b=c\iff a=?$

$$c-7b+b=(c-7b)^2+b^2$$

Rearrange to form a quadratic equation in $b$

As $b$ is real, the discriminant must be $\ge0$