Question

Solve the quadratic equation 6x^2-13x-28=0 by factoring.

Answer 1

First step to factor the trinomial, multiply the constant -28 with the leading coefficient 6.

So, -28 * 6 = - 168.

Next step is to breakdown -168 into two multiples so that their addition will result the coefficient of w= - 13.

So, -168 = -21 * 8.

And addition of - 21 and 8 will give - 13.

So, next step is to replace -13x with -21x + 8. Therefore,

6x² - 21x + 8x - 28 =0

(6x² - 21x) + (8x - 28 )=0 Make the group of two terms.

3x (2x - 7) + 4 (2x - 7) = 0 Take out the common factor from each group.

(2x - 7)(3x + 4) = 0 Again take out the common factor (2x -7).

So, 2x - 7 =0, 3x + 4 = 0 Set both the factor equal to 0.

2x = 7 , 3x = -4

So, $x= \frac{7}{2} , -\frac{4}{3}$

Hope this helps you !