Question

5x^2 − 24 = 26

APPROXIMATE ANSWERS X=______ OR X=_________
THE EXACT SOLUTIONS ARE ______ OR X=________

Answer 1

Approximation = 3 < x < 4 or -4 < x < -3

Exact Solution = 3.162 or -3.162

Explanation:

5x^2 - 24 = 26

First add 24 to both sides....

5x^2 = 50

Divide by 5...

x^2 = 10

Square root of 10 is exactly 3.162 or -3.162

Since 10 is not a perfect square, we can approximate it's square root by analyzing the perfect squares it is in between.

These perfect squares are 9 and 16

It looks like this:

`√(9) < √(10) < √(16)`

We know that the square roots of these numbers are 3 and 4 so that leaves us with this...

`3 < √(10) < 4`

Since we are dealing with square roots and perfect squares, we can also consider this as an option...

`-4 < √(10) < -3`