Question

Billie solved the equation below by completing the square, but she got the incorrect solution. In which step did Billie first make an error? Choices: 1234

Step 1: x^2+10x=49

Step 2: x^2+10x+25=49

Step 3: (x+5)^2=49

Step 4: x+5=+-7

Step 5: x=2, x=–12

Answer 1

step 2

Explanation:

we have

`x^(2) +10x-49=0` ---> given problem

step 1

Move the constant to the right side

`x^(2) +10x=49`

the step 1 is correct

step 2

Complete the square

`x^(2) +10x+5^2=49+5^2`

`x^(2) +10x+5^2=74`

The step 2 is not correct

step 3

Rewrite as perfect squares

`(x+5)^(2)=74`

step 4

take square root both sides

`x+5=\pm√(74)`

step 5

Find the values of x

`x=-5\pm√(74)`

`x=-5+√(74)`

`x=-5-√(74)`