Math

Question Find the values of xx that make 9x(x+8)=09x(x+8) = 0.

Studdy Solution

STEP 1

Assumptions
1. We are given the expression 9x(x+8)9x(x+8).
2. We want to find all values of xx that make this expression equal to 00.

STEP 2

To find the values of xx that make the expression equal to 00, we set the expression equal to 00.
9x(x+8)=09x(x+8) = 0

STEP 3

Apply the Zero Product Property, which states that if the product of two factors is zero, then at least one of the factors must be zero.
9x=0orx+8=09x = 0 \quad \text{or} \quad x+8 = 0

STEP 4

Solve the first equation for xx.
9x=09x = 0
x=09x = \frac{0}{9}
x=0x = 0

STEP 5

Solve the second equation for xx.
x+8=0x + 8 = 0
x=8x = -8

STEP 6

Combine the solutions from STEP_4 and STEP_5 to provide all values of xx that make the original expression equal to 00.
x=0andx=8x = 0 \quad \text{and} \quad x = -8
The values for xx that will make the expression 9x(x+8)9x(x+8) equal to 00 are x=0x = 0 and x=8x = -8.

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