Solve X^2 + 16X = 17 by completing the square

[LizzyLee88]

X^2 + 16X = 17

I am stumped.

 

[tkhunny]

No need to post the same problem in multiple locations.

Hint: 16/2 = 8
Another Hnt: 8^2 = 64

 

[stapel]

Was this topic not covered in class or in your textbook?

Eliz.

 

[LizzyLee88]

math is my weakest subject. this is my first year of college level math and i don't have a tutor this time. but thanks for the help, the exam is tonight. ahhhh :?

 

[dahmay]

X^2 + 16X = 17
THEN X^2 + 16X - 17 = 0
(X+17)(X-1) = 0
NOTE +17-1= +16
+17 * -1 = -17 XXXXXX :wink:

 

[jonboy]

X^2 + 16X = 17
THEN X^2 + 16X - 17 = 0
(X+17)(X-1) = 0
NOTE +17-1= +16
+17 * -1 = -17 XXXXXX :wink:

Well the title was to solve by competing the square.

 

[chapdawg147]

X^2+16x=17
X^2+16x-17=0

complete the square
first observe the value of the x variable, it is 16
the square of (a+b)^2=a^2+2abx+b^2
if you assume that 2abx=16x then a=x and b=8
(x+8)^2 is the square that you want to complete
(x+8)^2=x^2+16x+64
in your original equation you have x^2+16x you just need make -17 become 64
add 81 to both sides
x^2+16x-17+81=0+81

x^2+16x+64=81

(x+8)^2=81 take the square root of both sides
x+8=9 and x+8=-9
x=1 and x=-17

 

[tkhunny]

first observe the value of the x variable, it is 16

Coefficient?

if you assume that 2abx=16x then a=x and b=8

a=x? Are you reusing varable expressions? What does this mean?

(x+8)^2=81 take the square root of both sides
x+8=9 and x+8=-9

I'd prefer factoring to the mysterious appearance of two solutions using this methodology.

(x+8)^2 - 81 = 0
[(x+8)+9][(x+8)-9] = 0

Oh, THAT'S why there are two solutions!

Note: Welcome! Folks who want to help are appreciated from the beginning.