Question

Find all solutions for X and check. (different from the other question I asked earlier) thanks!

Answer 1

   
$\displaystyle \\ 17) \\ x(5x-10)=0 \\ x = 0 ~~\texttt{or}~~5x-10 = 0 \\ x_1 = \boxed{0} \\ \\ x_2 = \frac{10}{5} =\boxed{2} \\ \texttt{Check: } \\ x_1 = 0~~\Longrightarrow ~~ 0(5\cdot 0 - 10) = 0 \cdot (-10) = 0 \\ x_2 = 2~~\Longrightarrow ~~ 2(5\cdot 2 - 10) = 2(10 - 10) = 2 \cdot 0 = 0$


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