Question

How do you solve `(x + 7) ( 2x + 5) = - 7`?

Answer 1

`x=-6,-7/2`

Explanation:

Solve:

`(x+7)(2x+5)=-7`

Expand the left side using the FOIL method.

`2x^2+19x+35=-7`

Add `7` to both sides.

`2x^2+19x+35+7=0`

Simplify.

`2x^2+19x+42=0`

Factor the left-hand side.

`(x+6)(2x+7)=0`

Set each binomial equal to zero and solve.

`(x+6)=0`

`x=-6`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`(2x+7)=0`

`2x=-7`

Divide both sides by `2`.

`x=-7/2`

Answer 2

`x=-7/2=-3 1/2` or `x=-6`

Explanation:

`(x+7)(2x+5)=-7`

Expand the brackets.

`x(2x+5)+7(2x+5)=-7`

`2x^2+5x+14x+35=-7`

`2x^2+19x+35=-7`

Add `7` to both sides.

`2x^2+19x+35+7=7-7`

`2x^2+19x+42=0`

Factorise.

`2x^2+12x+7x+42=0`

`2x(x+6)+7(x+6)=0`

`(2x+7)(x+6)=0`

`2x+7=0` and `x+6=0`

`x=-7/2` or `x=-6`