To solve this equation, take the square root of each side.
-1/2±sqrt(15)/2
Practice makes perfect
Notice that on the left hand side of the given equation we have a perfect square trinomial. 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 c=- 12+ sqrt(15)2 and c=- 12- sqrt(15)2. To check our answer, let's find the related functions. We will write the first one using the two roots we found.
( c - ( - 1/2 + sqrt(15)/2) ) ( c - ( - 1/2 - sqrt(15)/2) ) ⇕ (c+1/2-sqrt(15)/2)(c+1/2+sqrt(15)/2)
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 c.
We see that only one graph appears. This means that both graphs coincide. Therefore, - 12+ sqrt(15)2 and - 12- sqrt(15)2 are correct solutions. âś“
