High School

Solve for [tex] a [/tex].

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

Select both solutions:

A. 196
B. 14
C. -196
D. -14

Answer :

Certainly! Let's solve the equation [tex]\(5a^2 = 980\)[/tex] following a step-by-step approach.

1. Start with the given equation:
[tex]\[
5a^2 = 980
\][/tex]

2. Divide both sides by 5 to isolate [tex]\(a^2\)[/tex]:
[tex]\[
a^2 = \frac{980}{5}
\][/tex]
[tex]\[
a^2 = 196
\][/tex]

3. Find the square roots of [tex]\(a^2 = 196\)[/tex]:

When we solve for [tex]\(a\)[/tex] by taking the square root, we consider both the positive and negative solutions:
[tex]\[
a = \sqrt{196} \quad \text{and} \quad a = -\sqrt{196}
\][/tex]

4. Calculate the square roots:
[tex]\[
a = 14 \quad \text{and} \quad a = -14
\][/tex]

So, the solutions for [tex]\(a\)[/tex] are [tex]\(14\)[/tex] and [tex]\(-14\)[/tex].