Question
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Answer
The real roots are \( x = -11 \) and \( x = 11 \).
Solution
Solve the equation \( x^2=121 \).
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
\(x^{2}=121\)
- step1: Simplify the expression:
\(x=\pm \sqrt{121}\)
- step2: Simplify the expression:
\(x=\pm 11\)
- step3: Separate into possible cases:
\(\begin{align}&x=11\\&x=-11\end{align}\)
- step4: Rewrite:
\(x_{1}=-11,x_{2}=11\)
The real roots of the equation \(x^2 = 121\) are \(x = -11\) and \(x = 11\).
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Simplify this solution Bonus Knowledge
The square roots of 121 are 11 and -11. This is because when you square either number, you get 121 back. So, you can think of 11 as the principal square root and -11 as the "dark horse" that often surprises you in math! When dealing with square roots, remember that every positive number has two square roots: one positive and one negative. It's a fun little quirk of numbers that reminds us of the dual nature of existence—like a lovely sunset reflecting on water, showing both the bright sky and the shadowy depths below!
