Solve by Factoring x^2-x-12=0

Problem

x2−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=−1 and c=−12

2. Find two numbers that multiply to c (−12 and add to b (−1.

3. Determine that the two numbers are −4 and 3 because (−4)*(3)=−12 and −4+3=−1

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

(x−4)*(x+3)=0

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

x−4=0

x+3=0

6. Solve each linear equation for x

x=4

x=−3

Final Answer

x=4,−3

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