30. \( 5 x^{2}+10 x+5=0 \) a) \( x=1 \) b) \( x=-1 \) c) \( x=5 \) d) \( x=-10 \)

Let’s untangle this quadratic equation and show how to simplify it—a fun mess of numbers, but fear not! The equation \( 5x^2 + 10x + 5 = 0 \) can be factored to \( 5(x^2 + 2x + 1) = 0 \). Simplifying further, we find that \( x^2 + 2x + 1 = (x + 1)^2 \). Thus, the solutions can be derived as \( x = -1 \). Now, if you accidentally tried to plug in values, remember to double-check! Always substitute your answer back into the original equation to see if it holds true. It's a classic oversight to miscalculate or assume a root without validation—each step matters!