Question

Please see attached photo for my problem from homework set. Thanks in advance!

Answer 1

Question:

Solution:

a) Consider the following equation:

`(x+4)(x-2)=7`

applying the distributive property, we get:

`x^2+2x-8\text{ =}7`

now, putting all terms on one side of the equation, we get:

`x^2+2x-8-7=0`

this is equivalent to:

`x^2+2x-15=0`

Factoring this expression, we get:

`(x-3)(x+5)=0`

according to the equation, we can conclude that the solutions for the given equation are:

`x\text{ = 3}`

and

`x=\text{ }-5`

b) Consider the following equation:

`6x^2+9x-22\text{ =0}`

applying the quadratic formula:

`\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

where

a = 6,

b = 9

and

c = -22,

we obtain that the solutions of the given equations are:

`x\text{ =}\frac{-9+\sqrt[]{609}}{12}=\text{ 1.3}0`

and

`x\text{ =}\frac{-9-\sqrt[]{609}}{12}=\text{ -2.8}0`