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 (which is −12 and add to b (which is 1.

3. Determine that the two numbers are 4 and −3 since 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

x2+x−12=0⇒x=−4,3

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