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:
[tex]\sqrt{9} < \sqrt{10} < \sqrt{16}[/tex]
We know that the square roots of these numbers are 3 and 4 so that leaves us with this...
[tex]3 < \sqrt{10} < 4[/tex]
Since we are dealing with square roots and perfect squares, we can also consider this as an option...
[tex]-4 < \sqrt{10} < -3[/tex]
