151. Solve the equation $x^{2}+4 x=77$.
151. $x_{1}=7 ; x_{2}=-11$ (solved geometrically by Al-Khwarizmi).

152 The general solution: $z^{2}$ $-14 z+48=0 ;$ from which $z_{1}=8 ; z_{2}=6$. Al-Khwarizmi constructs a rectangle $A D B C=$ $=48$ and a line $C F=14$ (Fig. 43). Then he constructs a square $K C F H$ on the latter. It is clear that $G H E B=48$, and the entire square $K C F H==196$, therefore:

$$
K A B G+B D F E=100=x^{2}+y^{2}
$$

but $2 x y=96$ and $(x-y)^{2}=4$, from which $x-y=2$, then it is easy to find $x$ and $y$. The second system is also solved in the same way.

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