To solve this equation take the square root of each side.
-2 and - 12
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 can simplify this result into two separate roots.
d=- 5 ±3/4
d_1=- 5-3/4
d_2=- 5+3/4
d_1=- 8/4
d_2=- 2/4
d_1=- 2
d_2=- 1/2
We found that the solutions to the given equation are - 2 and - 12. To check our answer, we will graph the related function y=16d^2+40d+16 using a calculator. Note that in the calculator we will use the variable x instead of d.
We can see that the x-intercepts are - 2 and - 12. Therefore, our solutions are correct.
