Question

Which of the following are solutions to the equation below?Check all that apply.x2 – 6x + 40 = 6x + 5

a. -5 b. -6 c. 7 d. 5 e. 6

Answer 1

x^2 - 6x + 40 = 6x + 5

x^2 - 6x + 40 -6x - 5 = 0 (move all terms to one side)

x^2 - 12x + 35 = 0

(x - 7)(x - 5) = 0

x = 7, 5

hope that helps, God bless!

Answer 2

c.7 and d.5

Explanation:

Given the following equation :

`x^(2)-6x+40=6x+5`

This equation is equivalent to the following equation :

`x^(2)-6x+40=6x+5`

`x^(2)-6x+40-6x-5=0`

`x^(2)-12x+35=0`

Given an equation
`ax^(2)+bx+c=0` we can find the solutions using the quadratic equation (x1 and x2 are the solutions) :

`x1=\frac{-b+\sqrt{b^(2)-4ac}}{2a}`

`x2=\frac{-b-\sqrt{b^(2)-4ac}}{2a}`

Using this equations :

`x^(2)-12x+35=0`

`a=1\\b=-12\\c=35` ⇒

`x1=\frac{-(-12)+\sqrt{(-12)^(2)-4.(1).(35)}}{2.(1)}=7`

`x2=\frac{-(-12)-\sqrt{(-12)^(2)-4.(1).(35)}}{2.(1)}=5`

Given the two solutions x1 and x2 we can write the equation :

`ax^(2)+bx+c=0` ⇒
`a.(x-x1).(x-x2)=0` ⇒

`x^(2)-12x+35=0` is equivalent to

`(x-7).(x-5)=0`

The solutions for this equation are 7 and 5.

Therefore, c.7 and d.5 are the solutions for this exercise.