Math  /  Algebra

QuestionSolve using the principle of zero products. (x+6)(x+4)=0(x+6)(x+4)=0
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x=x= \square (Simplify your answer. Use a comma to separate answers as needed.) B. There is no solution.

Studdy Solution

STEP 1

1. The equation (x+6)(x+4)=0(x+6)(x+4)=0 is a product of two linear factors set equal to zero.
2. The principle of zero products states that if a product of factors equals zero, at least one of the factors must be zero.

STEP 2

1. Apply the principle of zero products.
2. Solve each equation for xx.
3. Determine the solution set.

STEP 3

Apply the principle of zero products. Set each factor equal to zero:
x+6=0orx+4=0 x+6 = 0 \quad \text{or} \quad x+4 = 0

STEP 4

Solve each equation for xx:
For x+6=0x+6 = 0:
x=6 x = -6
For x+4=0x+4 = 0:
x=4 x = -4

STEP 5

Combine the solutions into a solution set. Since both values satisfy the original equation, we list them as the solutions:
x=6,4 x = -6, -4
The correct choice is:
A. x=6,4 x = -6, -4

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord