Question

How do you solve `25x ^ { 2} - 1= 48`?

Answer 1

See the entire solution process below:

Explanation:

FIrst, add `color(red)(1)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`25x^2 - 1 + color(red)(1) = 48 + color(red)(1)`

`25x^2 - 0 = 49`

`25x^2 = 49`

Next, divide each side of the equation by `color(red)(25)` to isolate the `x^2` term while keeping the equation balanced:

`(25x^2)/color(red)(25) = 49/color(red)(25)`

`(color(red)(cancel(color(black)(25)))x^2)/cancel(color(red)(25)) = 49/25`

`x^2 = 49/25`

Now, take the square root of each side of the equation to solve for `x` while keeping the equation balanced. Remember, when taking the square root of a number there is a positive and negative result:

`sqrt(x^2) = +-sqrt(49/25)`

`x = +-7/5`