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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.

User Skaushal
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Answer:

1: adding 7 to

2: 9

3: x-3

4: 4

User Mbask
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"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
User Mgibson
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