To solve the expression x2 + 6x + 4, we start by recognizing that we are dealing with a quadratic equation in the standard form of ax2 + bx + c, where a = 1, b = 6, and c = 4.
Next, we can examine this equation to check if it can be factored easily. We are looking for two numbers that multiply to 4 (the constant term) and add up to 6 (the coefficient of x). The pair of numbers that satisfy this condition is 2 and 2, since 2 * 2 = 4 and 2 + 2 = 4.
Now, we can rewrite the quadratic expression:
x2 + 6x + 4 = (x + 2)(x + 2) = (x + 2)2
This shows that the expression can be factored into a perfect square. The solution for x occurs when this equation is set to zero:
(x + 2)2 = 0
Solving for x gives:
x + 2 = 0 → x = -2
Thus, the quadratic equation x2 + 6x + 4 has a double root at x = -2.