Solve by Factoring x^2-4x-12=0

Problem

x2−4*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=−4 and c=−12

2. Find two numbers that multiply to c (−12 and add to b (−4.

3. Determine the factors by testing pairs of numbers: −6 and 2 satisfy both conditions because (−6)*(2)=−12 and −6+2=−4

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

(x−6)*(x+2)=0

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

x−6=0

x+2=0

6. Solve each linear equation for x

x=6

x=−2

Final Answer

x2−4*x−12=0⇒x=6,−2

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