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].
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].
