Question

Solve each equation by using the square root property. 2x^2–9=11

Answer 1

We want to solve

2x^2–9=11

First, isolate the portion of the equation that's actually being squared. That is:

2x^2 = 11 + 9

that is equivalent to:

2x^2 = 20

that is equivalent to

x^2 = 20/ 2 = 10

that is

x^2 = 10

Now square root both sides and simplify, that is:

`\sqrt[]{x^2\text{ }}=\text{ }\sqrt[]{10}`

we know that the square root is the inverse function of the function x^ 2, so we can cancel the square :

`x\text{ = }\sqrt[]{10}`

but note that there is always the possibility of two roots for every square root: one positive and one negative: so the final answer is:

`x\text{ = +/- }\sqrt[]{10}`