Answer :
To solve the equation [tex]\( x^2 - 5 = 139 \)[/tex], follow these steps:
1. Isolate the square term: You want to get [tex]\( x^2 \)[/tex] by itself on one side of the equation. To do this, add 5 to both sides:
[tex]\[
x^2 - 5 + 5 = 139 + 5
\][/tex]
This simplifies to:
[tex]\[
x^2 = 144
\][/tex]
2. Solve for [tex]\( x \)[/tex] by taking the square root: To find [tex]\( x \)[/tex], take the square root of both sides of the equation. Remember, taking the square root of a number gives two possible solutions: the positive and negative roots:
[tex]\[
x = \sqrt{144} \quad \text{or} \quad x = -\sqrt{144}
\][/tex]
3. Calculate the square roots: The square root of 144 is 12. Therefore, your solutions are:
[tex]\[
x = 12 \quad \text{or} \quad x = -12
\][/tex]
So, the solutions to the equation [tex]\( x^2 - 5 = 139 \)[/tex] are [tex]\( x = 12 \)[/tex] and [tex]\( x = -12 \)[/tex].
1. Isolate the square term: You want to get [tex]\( x^2 \)[/tex] by itself on one side of the equation. To do this, add 5 to both sides:
[tex]\[
x^2 - 5 + 5 = 139 + 5
\][/tex]
This simplifies to:
[tex]\[
x^2 = 144
\][/tex]
2. Solve for [tex]\( x \)[/tex] by taking the square root: To find [tex]\( x \)[/tex], take the square root of both sides of the equation. Remember, taking the square root of a number gives two possible solutions: the positive and negative roots:
[tex]\[
x = \sqrt{144} \quad \text{or} \quad x = -\sqrt{144}
\][/tex]
3. Calculate the square roots: The square root of 144 is 12. Therefore, your solutions are:
[tex]\[
x = 12 \quad \text{or} \quad x = -12
\][/tex]
So, the solutions to the equation [tex]\( x^2 - 5 = 139 \)[/tex] are [tex]\( x = 12 \)[/tex] and [tex]\( x = -12 \)[/tex].
