What is the intermediate step in the form (x+a)^2=b(x+a) 2
=b as a result of completing the square for the following equation?
6x^2+48x+207=15

The intermediate step are;

1) Separate the constants from the terms in x² and x

2) Divide the equation by the coefficient of x²

3) Add the constants that makes the expression in x² and x a perfect square and factorize the expression

Step-by-step explanation:

The function given in the question is 6·x² + 48·x + 207 = 15

The intermediate steps in the to express the given function in the form (x + a)² = b are found as follows;

6·x² + 48·x + 207 = 15

We get

1) Subtract 207 from both sides gives 6·x² + 48·x = 15 - 207 = -192

6·x² + 48·x = -192

2) Dividing by 6 x² + 8·x = -32

3) Add the constant that completes the square to both sides

x² + 8·x + 16 = -32 +16 = -16

x² + 8·x + 16 = -16

4) Factorize (x + 4)² = -16

5) Compare (x + 4)² = -16 which is in the form (x + a)² = b

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt