Solve the following equation using the perfect square trinomial pattern: x^2+x+0.25=0
To solve the equation x^2 + x + 0.25 = 0 using the perfect square trinomial pattern, we need to rewrite it in the form of (x + a)^2 = 0, where "a" is a constant.
First, we notice that the coefficient of x^2 is 1, implying that a = 1/2 (half the coefficient of x).
Next, we use the formula for squaring a binomial, (x + a)^2 = x^2 + 2ax + a^2, to expand the perfect square trinomial (x + a)^2:
(x + 1/2)^2 = x^2 + 2(1/2)x + (1/2)^2
(x + 1/2)^2 = x^2 + x + 1/4
Comparing this expanded form to the given equation, we see that (x + 1/2)^2 = 0. We know that any number squared equals 0 when that number is 0, so we have:
x + 1/2 = 0
Subtracting 1/2 from both sides:
x = -1/2
Therefore, the solution to the equation x^2 + x + 0.25 = 0 is x = -1/2.