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.
answers:
adding 7 to
9
x-3
4

Answers: Using the process of completing the square:

1. Isolate the constant by adding 7 to both sides of the equation:

x^2-6x-7+7=0+7

x^2-6x=7

2. Add 9 to both sides of x2 – 6x = 7 to form a perfect square trinomial while keeping the equation balanced:

x^2-6x+9=7+9

x^2-6x+9=16

3. Write the trinomial x2 – 6x + 9 as squared:

(x-3)^2 = 16

4. Use the square root property of equality to get x – 3 = ±4 .

sqrt[ (x-3)^2 ] = ± sqrt(16)

x-3 = ±4

5. Isolate the variable to get solutions of –1 and 7.

x-3 = ±4

x-3+3 = ±4+3

x = ±4+3

x1=-4+3→x1=-1

x2=+4+3→x2=7

1 adding 7 to

2 9

3 x-3

4 4

Step-by-step explanation:

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .