Question
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Answer
Las soluciones son \( a = 3 \) y \( a = -3 \).
Solution
Para resolver la ecuación \( 3 a^{2} = 27 \), seguimos estos pasos:
1. Dividimos ambos lados de la ecuación entre 3:
\[
a^{2} = \frac{27}{3}
\]
\[
a^{2} = 9
\]
2. Ahora, tomamos la raíz cuadrada de ambos lados:
\[
a = \pm \sqrt{9}
\]
\[
a = \pm 3
\]
Por lo tanto, las soluciones son \( a = 3 \) y \( a = -3 \).
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Simplify this solution Beyond the Answer
To solve for \( a \), first divide both sides of the equation \( 3 a^2 = 27 \) by 3. This simplifies the equation to \( a^2 = 9 \). Now, taking the square root of both sides, you find that \( a = 3 \) or \( a = -3 \). It's essential to consider both the positive and negative roots since squaring a negative number gives a positive result. A common mistake when solving quadratic equations is to forget to consider both the positive and negative roots after taking the square root. Another pitfall is to misinterpret the equation and mistakenly add or subtract terms incorrectly. Always double-check your steps to ensure all potential solutions are accounted for!
