Solve the following equation.

x^2 + 28x = 0
x = 1 (smaller value)
x = 2 (larger value)

x (x+28) = 0

x = 0 or x = -28

To solve the quadratic equation x^2 + 28x = 0, we can apply factoring.

First, we notice that both terms have a common factor of x. So we can factor out x from the equation:
x(x + 28) = 0

Now we have two factors, x and (x + 28), that multiply together to equal zero. According to the Zero Product Property, if the product of two factors is zero, then at least one of the factors must be zero.

So we set each factor equal to zero and solve for x:

1) x = 0

2) x + 28 = 0
Subtract 28 from both sides:
x = -28

Therefore, the solutions to the equation x^2 + 28x = 0 are x = 0 and x = -28.

The values you provided, x = 1 and x = 2, are not correct solutions to the equation.