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Solve for [tex] a [/tex].

[tex] 5a^2 = 980 [/tex]

Select both solutions.

A. [tex] -14 [/tex]
B. 14
C. 196
D. [tex] -196 [/tex]

Answer :

To solve the equation [tex]\(5a^2 = 980\)[/tex], we have to find the values of [tex]\(a\)[/tex] that satisfy this equation. Here's how we can do it step by step:

1. Divide both sides by 5:

Start by simplifying the equation [tex]\(5a^2 = 980\)[/tex] by dividing both sides by 5 to isolate [tex]\(a^2\)[/tex]:

[tex]\[
a^2 = \frac{980}{5}
\][/tex]

Calculate the right side:

[tex]\[
a^2 = 196
\][/tex]

2. Solve for [tex]\(a\)[/tex]:

To find [tex]\(a\)[/tex], take the square root of both sides. Remember that the square root operation can yield both a positive and a negative solution:

[tex]\[
a = \sqrt{196} \quad \text{or} \quad a = -\sqrt{196}
\][/tex]

Calculate the square roots:

[tex]\[
a = 14 \quad \text{or} \quad a = -14
\][/tex]

Therefore, the solutions for the equation [tex]\(5a^2 = 980\)[/tex] are [tex]\(a = 14\)[/tex] and [tex]\(a = -14\)[/tex]. The correct answers from the given options are [tex]\(14\)[/tex] and [tex]\(-14\)[/tex].

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