How do you solve by factoring # 2x^2+ 7x + 3=0#?

Question

Eva Abramson · Accepted Answer

#x=-3#
#x=-1/2# #2x^2+7x+3=0# or #2x^2+6x+x+3=0# or #2x(x+3)+1(x+3)=0# or #(x+3)(2x+1)=0# or #x+3=0# #x=-3#=======Ans #1# or #2x+1=0# or #2x=-1# or #x=-1/2#======Ans #2#

Kennedy Adams · Answer

undefined To solve the quadratic equation 2x^2 + 7x + 3 = 0 by factoring, follow these steps:

1. Identify the quadratic equation in the form ax^2 + bx + c = 0.
2. Multiply the coefficient of x^2 (a) by the constant term (c). In this case, 2 * 3 = 6.
3. Find two numbers that multiply to give the product obtained in step 2 (6) and add to give the coefficient of x (b), which is 7 in this case. The numbers are 6 and 1.
4. Rewrite the middle term (7x) using the two numbers found in step 3. So, 7x can be written as 6x + 1x.
5. Rewrite the quadratic equation with the new expression from step 4: 2x^2 + 6x + 1x + 3 = 0.
6. Group the terms in pairs: (2x^2 + 6x) + (1x + 3) = 0.
7. Factor out the greatest common factor from each pair: 2x(x + 3) + 1(x + 3) = 0.
8. Notice that both terms now have a common factor of (x + 3).
9. Factor out (x + 3): (2x + 1)(x + 3) = 0.
10. Set each factor equal to zero and solve for x: 
   - 2x + 1 = 0 => 2x = -1 => x = -1/2
   - x + 3 = 0 => x = -3

So, the solutions to the equation 2x^2 + 7x + 3 = 0 are x = -1/2 and x = -3.