Homework Help

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

user profile pic

pavelpimen | Student, Undergraduate | Honors

Posted October 11, 2010 at 9:27 PM via web

dislike 0 like

Solve the quadratic. (don't use formula)

7x^2+10x+3=0

Tagged with math

4 Answers | Add Yours

user profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted October 11, 2010 at 9:35 PM (Answer #1)

dislike 9 like

let f(x) = 7x^2 + 10x + 3

Let us factor:

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

Then we have 2 solutions:

x1= -3/7

x2 = -1

user profile pic

giorgiana1976 | College Teacher | Valedictorian

Posted October 11, 2010 at 9:28 PM (Answer #2)

dislike 1 like

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}

user profile pic

william1941 | College Teacher | Valedictorian

Posted October 11, 2010 at 9:34 PM (Answer #3)

dislike 0 like

As we have to find the roots of the quadratic equation 7x^2 + 10x + 3 =0, without using the formula for finding the roots, we go about it this way.

First express 10x as two terms the product of which is 7x^2*3 = 21x^2.

We see that 10x can be written as 7x + 3x and 7x*3x = 21x^2

So we write the given equation as:

7x^2 + 10x + 3 =0

=> 7x^2 + 7x + 3x + 3 =0

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

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

=>  7x+3 = 0  or x+1 =0

=> x = -3/7 or x= -1

Therefore the values of x we get are -1 and -3/7.

user profile pic

phucnguyen08 | Student , College Freshman | Honors

Posted October 12, 2010 at 6:16 AM (Answer #5)

dislike 0 like

7x^2+7x+3x+3=o

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

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

x+1=0        x=-1

7x+3=0       x=-3/7

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes