Complete each statement in the steps to solve x2 – 6x – 7 = 0 using the process of completing the square.

x = -1, 7

Step-by-step explanation:

Given question is incomplete; find the complete question in the attachment.

x² - 6x - 7 = 0

Step 1,

Isolate the constant by ADDING 7 both the sides of the equation.

x² - 6x - 7 + 7 = 0 + 7

x² - 6x = 7

Step 2

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

x² - 6x + 9 = 7 + 9

Step 3

Write the trinomial x² - 6x + 9 as (x - 3) squared.

x² - 2(3)x + 9 = 16

(x - 3)² = 4²

Step 4

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

(x - 3)² = 4²

(x - 3) = ±4

Step 5

Isolate the variable to get solution of -1 and 7

x - 3 = ± 4

x = -3 ± 4

x = -1, 7

The ODE is separable:

Integrate both sides to get

Assuming the bubble starts with zero volume, so that , we find

Then the volume of the bubble at time is

and so the time it take for the bubble to reach a volume of 629 cubic cm is

or 23 seconds after the teen first starts blowing the bubble.