Solve each equation below by completing the square:
1) x^2 + 6x = 16
My steps:
x^2 + 6x - 16 = 0
(x - 2 )(x + 8)
x = 2, -8
I set it to zero and factored it out. But my teacher said not do it that way and do it by dividing by 2 but I don't understand how that works. I got the right answer but not the right way to solve it? If someone could explain how to do it by dividing it by 2, that would be awesome. Thank you!
I know I got the x = 2 -8 correct so I don't understand how you got x = -3±5 or where the 9 came from.
(x+a)^2 = x^2+2ax+a^2
To solve the equation x^2 + 6x = 16 by completing the square, you need to follow these steps:
1. Move the constant term to the right side of the equation, so you have x^2 + 6x - 16 = 0.
2. Divide the coefficient of x by 2 and square the result. In this case, (6/2)^2 = 9.
3. Add the value obtained in step 2 to both sides of the equation. x^2 + 6x + 9 = 16 + 9 simplifies to x^2 + 6x + 9 = 25.
4. Express the left side as a perfect square trinomial. Since the left side is already a perfect square trinomial, it simplifies to (x + 3)^2 = 25.
5. Take the square root of both sides of the equation. x + 3 = ±√25, which gives x + 3 = 5 and x + 3 = -5.
6. Solve for x by isolating it on each side of the equation. x = 5 - 3 gives x = 2, and x = -5 - 3 gives x = -8.
So the solutions to the equation x^2 + 6x = 16 are x = 2 and x = -8.
The method your teacher suggested of dividing the coefficient of x by 2 is used to determine the number to add and subtract to complete the square. In this case, dividing 6 by 2 gives 3, which is then squared to get 9. Adding and subtracting 9 from both sides completes the square.
you were supposed to complete the square.
x^2 + 6x = 16
x^2 + 6x + 9 = 16+9
(x+3)^2 = 25
x+3 = ±5
x = -3±5
and you get your solution.
To complete the square, you divide the coefficient of x by 2, since (x+a)^2 = a^2+2ax+a^2.
Look. You had
x^2+6x
If you consider that as x^2+2ax, a=3.
to complete the square, you have to add a^2, which is 9.
Just follow the steps I took in my solution. I assume you can take the square root of 25 when you get that far...