Question

Solve the following quadratic equation using the perfect square trinomial pattern: 14x2+2x+4=0
1
4
𝑥
2
+
2
𝑥
+
4
=
0
.(1 point)
x=
𝑥
=

Answer 1

Interpret the equation as (1/4)x^2 + 2x + 4 = 0. Multiply both sides by 4 to clear the fraction:

x^2 + 8x + 16 = 0

This is a perfect square trinomial: (x + 4)^2 = 0, so

x + 4 = 0 ⇒ x = −4.

(Repeated root: x = −4.)