solve by completing the square??

Question

solve by completing the square??
x^2+8x=9

im stuck on this problem someone please help

Answer 1

x² + 8x = 9

x² + 8x + _____= 9 + _____

x² + 8x + 16 = 9 + 16

(x + 4) (x + 4) = 25

(x + 4) ² = 25

(√x + 4) ² = ± √25

x + 4 = ± 5

Transpose 4

x + 4 - 4 = - 4 ± 5

x = - 4 ± 5

- - - - - - -

solving for +

x = - 4 + 5

x = 1

- - - - - - - --

solving for -

x = - 4 - 5

x = - 9

- - - - - - - -s-

Answer 2

Completing the square means adding something to both sides that makes the side with x in it a perfect square. In this case, you add 16.

x^2 + 8x = 9
x^2 + 8x + 16 = 9 + 16
(x+4)^2 = 25
taking the square root of both sides
x+4 = +/- 5

x+4 = 5
x = 1

x+4 = -5
x = -9

How did I know to use 16? I just took half of 8 and squared it. Works every time.

Incidentally, it would have been easier to solve this problem by factoring.
x^2 + 8x - 9 = 0
(x-1)(x+9) = 0

x-1 = 0
x = 1

x+9 = 0
x = -9

Answer 3

x^2+8x=9
x^2 +8x + 16 = 9 + 16
x^2 + 8x + 16 = 25
(x+4)^2 = 5^2
x+4 +/-5 = 0
x + 9 = 0; x - 1 = 0
x = -9, 1

When it says to complete the square, you add or subtract enough to make the x^2 + nx part into a perfect square.

Divide the term with the x in it (8x here) by two, and then square that. If you add that amount, it will give you a perfect square on one side of the equation. Add the same amount to the other side, then take square roots of each side. Remember that a number has both positive and negative roots. That's it.

Answer 4

x=1

Answer 5

To complete a square, you need a constant k for which 2 sqrt(k) = coeffient of the "x" term. In this case, k= 16. So we would have
(x+4)^2 = 9+16 (gotta do on the other side what you did on the variable side).
x+4 = +/- 5 (take equare roots)
x= -9 or +1

Answer 6

1. Take half of the coefficient of the x term and call it H. In this case, H = 8/2 or 4.
2. Square H and add it to the right side. In this case, the right side becomes 9+16 or 25.
3. The roots are plus or minus the square root of the right side minus H. In this case, the roots are 5 - 4 and -5 - 4, or 1 and -9.

Answer 7

There is a an easier way than compeleting the square..

substract 9 from both sides:
x^2+8x-9=0
(x-1)(x+9) = 0
x-1 = 0 then x = 1
OR x+9 = 0 then x = -9
so x = (1,-9)

Hope i helped you...

Answer 8

x² + 8x + 16 = 9 + 16
(x + 4)² = 25
x + 4 = ± 5
x = - 4 + 5 , x = - 4 - 5
x = 1 , x = - 9

Answer 9

x^2+8x=9
divide 8/2=4 then square it 16
(x+4)^2=9+16
(x+4)^2=25
x+4=+-5
x=-9 or x=1

You could have solved this problem easier by
x^2+8x-9=0
(x+9)(x-1)
x=-9 x=1

Answer 10

x^2+8x=9
x^2+8x+16 = 9+16
(x+4)^2 = 25
x+4 = +/- sqrt(25)
x+4 = +/- 5
x = -4 +/- 5
x = -4+5 = 1
x = -4 -5 = -9