[tex]\displaystyle \\
17) \\
x(5x-10)=0 \\
x = 0 ~~\texttt{or}~~5x-10 = 0 \\
x_1 = \boxed{0} \\ \\
x_2 = \frac{10}{5} =\boxed{2} \\
\texttt{Check: } \\
x_1 = 0~~\Longrightarrow ~~ 0(5\cdot 0 - 10) = 0 \cdot (-10) = 0 \\
x_2 = 2~~\Longrightarrow ~~ 2(5\cdot 2 - 10) = 2(10 - 10) = 2 \cdot 0 = 0 [/tex]
[tex]\displaystyle 18) \\
x^2 + 7x-18 = 42 \\
x^2 + 7x-18 - 42 =0 \\
x^2 + 7x-60 =0 \\
.~~~~~7x = 12x - 5x \\
\underbrace{x^2 + 12x} -\underbrace{5x - 60} = 0 \\ \\
x(x+12) -5(x+12)=0 \\
(x+12)(x-5)=0 \\
x + 12 = 0 ~~\texttt{or}~~x-5 = 0 \\ \\
x_1 = \boxed{-12} \\
x_2 = \boxed{5} \\ \\
\texttt{Check: } \\
x1 = -12 ~~\Longrightarrow~~ (-12)^2 + 7\cdot (-12)-18 = 144-84-18 = 42 \\ \\
x2 = 5 ~~\Longrightarrow~~ (5)^2 + 7\cdot (5)-18 = 25+35-18 = 42 \\ \\ [/tex]
