To solve this equation, take the square root of each side.
-5±sqrt(47)
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 -5+sqrt(47), and -5-sqrt(47). To check our answer, let's find the related functions. We will write the first one using the two roots we found.
(z-( - 5 + sqrt(47)))(z-( - 5 - sqrt(47))) ⇕ (z+5-sqrt(47))(z+5+sqrt(47))
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 z.
We see that only one graph appears. This means that both graphs coincide. Therefore, -5+sqrt(47) and -5-sqrt(47) are correct solutions. ✓
