Solve the following quadratic equation using the perfect square trinomial pattern: 1/4x^2+x+4 .(1 point) x=
To solve the quadratic equation 1/4x^2 + x + 4, we need to rewrite it in the form (ax + b)^2 + c.
Starting with the given equation:
1/4x^2 + x + 4
Next, we can complete the square by taking the coefficient of x (which is 1), dividing it by 2, and squaring it.
1/4 * (1/2)^2 = 1/16
Now we add this value to both sides of the equation:
1/4x^2 + x + 4 + (1/16) = (1/4x^2 + x + 1/16) + 4
Simplifying the right side:
1/4x^2 + x + 1/16 + 64/16 = 1/4x^2 + x + 65/16
Combining like terms on the right side:
1/4x^2 + x + 65/16
Now we have the equation in the form (ax + b)^2 + c, where a = 1/4, b = 1, and c = 65/16.
So the solution is x = -b/a = -(1)/(1/4) = -4.