Solving square roots property

Question

Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators.

2x² = 26

Answer 1

Solving by the square root property basically means to isolate x² (or in some cases (kx+c)², take the square root of both sides (where right side is greater than or equal to zero), then solve the remaining linear equation for one or two values of x.

For this problem it is easy to isolate x² (just divide both sides by 2).

x²=13

Since 12 is positive it has two square roots.

x=±√13.

Since 13 does not contain any perfect square factors you are done.

If you happen to be dealing with complex numbers the right side can also be negative.

Here is a more complicated example of using the square root property.

(2x-7)² - 5 = 15

(2x-7)²=20

2x-7 = ±√20

2x=7±√20

x = (7±√20)/2

All that remains is to place √20 in simplest radical form: 2√5.

So one root is:

(7+2√5)2

and the other is (7-2√5)/2

Answer 2

2x^2 = 26

x^2 = 26/2

x^2 = 13

x =-sqr13 or sqr13

x= about -3.61 or +3.61