Homework Help

x^2 + 8x -78=-5 Solve by completing the square.

user profile pic

rosey-girl | Student, Grade 12 | Valedictorian

Posted March 6, 2013 at 12:11 AM via web

dislike 1 like

x^2 + 8x -78=-5

Solve by completing the square.

2 Answers | Add Yours

user profile pic

jgeertz | College Teacher | (Level 1) Associate Educator

Posted March 6, 2013 at 12:53 AM (Answer #2)

dislike 1 like

`x^2+8x-78=-5`

Add `78` to both sides.

`x^2+8x= 73`

In order to create a trinomial square on the left side of the equation, add a value to both sides that is equal to the square of half the coefficient of `x` . In this case, add `4^2` to both sides.

`x^2+8x+16=73+16`

`x^2+8x+16=89`

Now factor the perfect trinomial square.

`(x+4)^2 =89`

Take the square root of each side of the equation.

`(x+4)^(2/2) = +-sqrt89`

`x+4 =+-sqrt89`

`x= +sqrt89 -4`

`x=-sqrt89 -4` 

The complete solution is:

`x=sqrt89 - 4, -sqrt89-4`

user profile pic

rosey-girl | Student, Grade 12 | Valedictorian

Posted March 6, 2013 at 12:12 AM (Answer #1)

dislike 0 like

Solve each equation by completing the square.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes