Consider the following quadratic equation:
x^2+14x+49=0
Step 2 of 2 : Solve the quadratic equation by factoring. Write your answer in reduced fraction form, if necessary.
To solve the quadratic equation by factoring, we need to find two numbers whose sum is 14 and whose product is 49.
The two numbers that satisfy these conditions are 7 and 7.
Therefore, the quadratic equation can be factored as:
(x + 7)(x + 7) = 0
Simplifying the equation further, we have:
(x + 7)^2 = 0
To solve for the value of x, we take the square root of both sides:
√(x + 7)^2 = √0
x + 7 = 0
Subtracting 7 from both sides, we have:
x = -7
So, the value of x that solves the quadratic equation x^2 + 14x + 49 = 0 is x = -7.