Solve by Factoring x^2+7x+12=0

Problem

x2+7*x+12=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0 where a=1 b=7 and c=12

2. Find two numbers that multiply to equal c (12) and add to equal b (7).

3. Determine that the two numbers are 3 and 4, since 3⋅4=12 and 3 + 4 = 7$.

4. Rewrite the quadratic expression as a product of two binomials using these numbers.

(x+3)*(x+4)=0

5. Apply the Zero Product Property by setting each binomial factor equal to zero.

x+3=0

x+4=0

6. Solve each linear equation for x

x=−3

x=−4

Final Answer

x=−3,−4

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