Question

5x^2 − 24 = 26

Answer 1

Answer:

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

Exact Solution = 3.162 or -3.162

Step-by-step 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:

$\sqrt{9} < \sqrt{10} < \sqrt{16}$

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

$3 < \sqrt{10} < 4$

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

$-4 < \sqrt{10} < -3$