Solve the quadratic. (don't use formula) 7x^2+10x+3=0

We'll have to solve the quadratic equation
7x^2+10x+3=0.

Since the request is not to apply the
quadratic formula, we'll use factorization.

We notice that
the coefficient of the middle term could be written as the sum of coefficients of the
first and the last terms.

 10 = 7 +
3

We'll multiply by x both
sides:

10x = 7x + 3x

We'll
re-write the equation:

 7x^2 + 7x + 3x + 3 =
0

We'll combine the first 2 terms and the last 2
terms:

 (7x^2 + 7x) + (3x + 3) =
0

We'll factorize by 7x the first pair of brackets and
we'll factorize by 3 the second pair of brackets.

7x(x+1) +
3(x+1) = 0

We'll factorize by
(x+1):

(x + 1)(7x + 3) =
0

We'll put each factor as
zero:

x+1 = 0

x1
= -1

7x + 3 =
0

7x = -3

x2 =
-3/7

The roots of the
quadratic equation are: {-1 ; -3/7}