Question
30. \( 5 x^{2}+10 x+5=0 \) a) \( x=1 \) b) \( x=-1 \) c) \( x=5 \) d) \( x=-10 \)
Ask by Gibson Lee. in the United States
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The answer is \( x = -1 \), choice b).
Solution
We start with the equation
\[
5x^2 + 10x + 5 = 0.
\]
Dividing both sides by \(5\) (which is valid because \(5 \neq 0\)) gives
\[
x^2 + 2x + 1 = 0.
\]
Notice that the quadratic can be factored as a perfect square:
\[
(x + 1)^2 = 0.
\]
Taking the square root on both sides, we obtain
\[
x + 1 = 0.
\]
Thus, the solution is
\[
x = -1.
\]
Among the options given, the correct answer is:
b) \( x = -1 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Extra Insights
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!
