Question

What are the roots of this quadratic equation? 2x2 5x = x2 7x 35

Answer 1

Answer:

x=-5, x=7

Step-by-step explanation:

We have the quadratic equations,

$2x^2+5x=x^2+7x+35$

We can rewrite this equation as

$2x^2-x^2+5x-7x-35=0\\\\x^2-2x-35=0$

We can solve for x using AC method.

AC = -35

B = -2

The factor pairs of 35 are

1×35, 7×5

Among these two, when we subtract 7 form 5, we get the middle term -2

Hence, -2x=-7x+5x

$x^2-7x+5x-35=0\\\\\text{Take GCF}\\\\x(x-7)+5(x-7)=0\\\\\text{Factor out the common terms}\\\\(x-7)(x+5)=0\\\\x=-5,7$

Thus, the roots are -5 and 7