Question

find all the values for x that will make this expression equal to 0. 9x(x + 8) after you enter your answer press go. x = and go

Explanation:

Step1: Set the expression equal to 0

We start with the equation \( 9x(x + 8)=0 \).

Step2: Apply the zero - product property

The zero - product property states that if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \) (or both). For the equation \( 9x(x + 8)=0 \), we can consider three factors: 9, \( x \), and \( x + 8 \). Since 9 is a non - zero constant, we set the other two factors equal to zero.

• Case 1: Set \( x=0 \). If \( x = 0 \), then \( 9\times0\times(0 + 8)=0\times8 = 0 \), so \( x = 0 \) is a solution.
• Case 2: Set \( x + 8=0 \). Solving for \( x \), we subtract 8 from both sides of the equation \( x+8 = 0 \), getting \( x=-8 \). When \( x=-8 \), we have \( 9\times(-8)\times(-8 + 8)=9\times(-8)\times0 = 0 \), so \( x=-8 \) is also a solution.

Answer:

\( x = 0 \) and \( x=-8 \)