Solve the following quadratic equation using the perfect square trinomial pattern: 1/4 x^2 + 2x + 4 = 0

1 answer

To solve the quadratic equation 14x2+2x+4=0 using the perfect square trinomial pattern, we first want to express it in a form that allows us to factor it as a perfect square.

  1. Start by eliminating the fraction. We can multiply the entire equation by 4 to make calculations easier:

4(14x2+2x+4)=40 x2+8x+16=0

  1. Now the equation is x2+8x+16=0. Notice that x2+8x+16 is a perfect square trinomial. It can be factored as:

(x+4)2=0

  1. Now, solve for x by taking the square root of both sides:

x+4=0

  1. Subtract 4 from both sides:

x=4

Thus, the solution to the equation 14x2+2x+4=0 is:

4