To solve this equation, take the square root of each side.
4±sqrt(7)
Practice makes perfect
To solve a quadratic equation in the form x^2=n, we will take the square root of each side. For any number n≥ 0, if x^2=n, then x=±sqrt(n). Keeping this in mind let's consider the given equation.
We found that the solutions to the given equation are 4+sqrt(7) and 4-sqrt(7). To check our answer, let's find the related functions. We will write the first one using the two roots we found.
(y-( 4 + sqrt(7)))(y-( 4 - sqrt(7))) ⇕ (y-4-sqrt(7))(y-4+sqrt(7))
To find the second one we will use the given equation.
Now we will graph the related functions in the same coordinate plane using a graphing calculator. Note that in the calculator we will use the variable x instead of y.
We see that only one graph appears. This means that both graphs coincide. Therefore, 4+sqrt(7) and 4-sqrt(7) are correct solutions. âś“
