Solve by Factoring x^2-x-6=0

Problem

x2−x−6=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=−6

2. Find two numbers that multiply to c (which is −6 and add to b (which is −1.

3. Determine that the two numbers are −3 and 2 since (−3)*(2)=−6 and −3+2=−1

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

(x−3)*(x+2)=0

5. Apply the zero product property by setting each factor equal to zero.

x−3=0

x+2=0

6. Solve each linear equation for x

x=3

x=−2

Final Answer

x=3,−2

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