Question

Complete each statement in the steps to solve x2 – 6x – 7 = 0 using the process of completing the square. Isolate the constant by both sides of the equation. Add to both sides of x2 – 6x = 7 to form a perfect square trinomial while keeping the equation balanced. Write the trinomial x2 – 6x + 9 as squared. Use the square root property of equality to get x – 3 = ±. Isolate the variable to get solutions of –1 and 7.

Answer 1

1: adding 7 to

2: 9

3: x-3

4: 4

Answer 2

"Isolate the constant by adding 7 to both sides of the equation."
This step separates the non-squareable 7 and the squareable
`x^2 - 6x` .

"Add 9 to both sides of
`x^2 - 6x = 7` to form a perfect square trinomial while keeping the equation balanced."
After separating the non-squareable, add the number which makes the first or left side a perfect square trinomial. The formula to find the number is:
`c = {(b)/(2) }^(2)` .
When we plug the values:
`c = { ( - 6)/(2) }^(2)`
Simplify:
`c = {( - 3)}^(2) = 9`

"Write the trinomial
`x^2 - 6x + 9` as
`(x - 3)` squared."
When you factor
`x^2 - 6x + 9` , you will get
`(x - 3) * (x - 3)` .

"Use the square root property of equality to get
`x - 3 = ± √(16)` ."
The 16 is coming from the part when we add 9. We needed 9 on the left side for a perfect square, but to protect the balance of the equality, we need to add 9 to the right side too. When we add 7 and 9, we got 16, and that is where it came from.

"Isolate the variable x to get solutions of -1 and 7."
To isolate x we branched the plus-minus sign:

`x - 3 = 4 \: \: \: x = 4 + 3 = 7 \\ \\ x - 3 = - 4 \: \: \: x = - 4 + 3 = - 1`