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

"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: $c = {\frac{b}{2} }^{2}$ .
When we plug the values: $c = { \frac{ - 6}{2} }^{2}$
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 $(x - 3) \times (x - 3)$ .

"Use the square root property of equality to get $x - 3 = ± \sqrt{16}$ ."
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:
$x - 3 = 4 \: \: \: x = 4 + 3 = 7 \\ \\ x - 3 = - 4 \: \: \: x = - 4 + 3 = - 1$

Answer 2

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Step-by-step explanation: