Question

Solve the quadratic equation by factoring x²+4x=0

Answer 1

To solve x²+4x=0 by factoring, factor out the common x to get x(x+4)=0, then apply the zero-product property to find x=0 and x=-4 as the solutions.

Step-by-step explanation:

To solve the quadratic equation by factoring x²+4x=0, we can apply the factoring technique. Factoring involves finding two expressions that multiply together to give the original expression. In this case, we notice that x is a common factor of both terms in the equation:

x(x + 4) = 0

This gives us two factors, x and (x + 4). According to the zero-product property, if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero:

• x = 0
• x + 4 = 0

From the first factor, we get x = 0. From the second factor, by subtracting 4 from both sides, we get x = -4.

Thus, the solutions to the equation are:

• x = 0
• x = -4