How do you solve x^2 - 21 = 3(5 - x^2)?

1 Answer
Mar 28, 2018

x=+- 3

Explanation:

We want to expand the brackets firstly:

3 xx 5=15

3xx-x^2=-3x^2

This, therefore:

x^2-21=3(5-x^2) -> x^2-21=15-3x^2

As we want to isolate the x to one side, we do not want -3x^2, and therefore we do the opposite which is to +3x^2. Notice that these cancel out. Also, remember what we do to one side we must do to another.

x^2-21=15-3x^2 -> 4x^2-21=15

We do not want -21, as we would like to get x on its own, and therefore do the opposite to -21 which is to +21, notice the -21+21 cancels out. Also, remember what you do to one side you MUST do to another.

4x^2-21=15 -> 4x^2=36

As we would like the value of x, first we realise we have 4 lots of x and divide both sides by 4

4x^2=36 -> x^2=9

As we would like x, we need to sqrt as that it the opposite to ^2, notice the ^2 cancels out. Also, remember to do this to both sides. We must also remember to take both square roots as they both satisfy the original equation

x^2=9 -> x=+-sqrt9=+-3

therefore x=+-3