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 using the perfect square trinomial pattern, we need to rewrite the equation in the form of (a + b)^2 = 0.
Starting with the given equation:
1/4x^2 + x + 4 = 0
To make the left side of the equation match the perfect square trinomial pattern, we need to complete the square.
First, divide the entire equation by 1/4 to get rid of the fractional coefficient:
(1/4) * (1/4x^2 + x + 4) = (1/4) * 0
1/16x^2 + 1/4x + 1 = 0
Now, focus on the first two terms: 1/16x^2 + 1/4x
To complete the square for these terms, take half of the linear coefficient (1/4), which gives 1/8, and then square it:
(1/8)^2 = 1/64
Add this value to both sides of the equation:
1/16x^2 + 1/4x + 1/64 = 1/64
Now, rewrite the left side of the equation as a perfect square trinomial:
(1/4x + 1/8)^2 = 1/64
Take the square root of both sides of the equation to isolate x:
[(1/4x + 1/8)]^(1/2) = (1/64)^(1/2)
1/4x + 1/8 = 1/8
Subtract 1/8 from both sides of the equation:
1/4x = 0
Divide both sides of the equation by 1/4 to solve for x:
x = 0
Therefore, the solution to the quadratic equation 1/4x^2 + x + 4 using the perfect square trinomial pattern is x = 0.