Question

How do you solve `2b ^ { 2} - 5= 103`?

Answer 1

See the entire solution process below:

Explanation:

First, add `color(red)(5)` to each side of the equation to isolate the `b` term while keeping the equation balanced:

`2b^2 - 5 + color(red)(5) = 103 + color(red)(5)`

`2b^2 - 0 = 108`

`2b^2 = 108`

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

`(2b^2)/color(red)(2) = 108/color(red)(2)`

`(color(red)(cancel(color(black)(2)))b^2)/cancel(color(red)(2)) = 54`

`b^2 = 54`

Now, take the square root of each side of the equation to solve for `b` while keeping the equation balanced. Remember, the square root of a number produces a negative and positive answer:

`sqrt(b^2) = +-sqrt(54)`

`b = +-sqrt(54) = +-7.348` rounded to the nearest thousandth.