X^2-8x=0 complete the square

Question

Complete the square 

Answer 1

Solve:    x² - 8x = 0   by Completing the Square

 

With the form, ax² + bx + c = 0,

   (1)  move constant to right side:

            ax² + bx = c       

   (2)  divide by a:

               x² + (b/a)x = -c/a 

   (3) add  ((b/a)/2)² to both sides:

          x² + (b/a)x + ((b/a)/2)² = -c/a +((b/a)/2)²

   (4)  take the square root of both sides:

          (x+ ((b/a/2))² = ± ( -c/a + ((b/a/2)² )

 

Let's do this!

   (1) already there

   (2) already done

 

   (3)  x² - 8x + 16 = 16

 

   (4)  (x-4)(x-4) = 16

          (x-4)² = 16

           x - 4 = ± 4

 

         So, either

             x - 4 = +4        or       x - 4 = -4

                x = 8           or        x = 0

 

Checking (very important):

  If the solution is x=8 or x=0, then

    (x-8)(x) = 0   ?   [multiplicative property of 0]

     x² - 8x  = 0   ?    yes, Distributive Property

Answer 2

If x² - 8x is to be altered in order to make it a perfect square, the linear term (-8x) gives the necessary clue as to what the constant term must be.

 

In the perfect square of the binomial (a + b)²  = a² + 2ab + b².

 

if 2ab = -8x and a = x then 2(x)b  = -8x  b = -4.

 

b² = (-4)² = 16

 

so, to complete the square, you must add 16 to both sides if the equation.

 

x² - 8x + 16 = 16

 

(x - 4)² - 16 = 0

Answer 3

Hi Madison.

 

When we complete the square we want to end up with a quadratic that can be factored in the form (x+a)² or (x-a)²

 

To do this we work with the coefficient of x, not x².

1) divide it by 2

2) take the result of 1) and square it.

3) add the result of 2) and add it to both sides of the equation.

 

So the coefficient of x is -8

-8/2 = -4

(-4)² = 16

 

x²-8x = 0

x²-8x + 16 = 0 + 16

x²-8x+16 = 16

 

If we factor the left side, we have

(x-4)(x-4) = 16

 

Which is equivalent to 

(x-4)² = 16

and

(x-4)² = 4²

 

Now if we take the square root of both sides we have

x-4 = 4

 

and 

x = 8