Question

PLS REPLY FAST NO EXPLAINATION NEEDED

Tony solved the equation below by completing the square, but he got the incorrect solution. In which step did Tony first make an error?
Step 1 : x 2 + 4 x = 77
Step 2 : x 2 + 4 x + 4 = 81
Step 3 : ( x + 2 ) 2 = 81
Step 4 : x + 2 = ± 81
Step 5 : x = 79 , x = − 83

Answer 1

The error made by Tony is in Step 4, where he wrote "x + 2 = ± 81". The correct step should be:

Step 4: Take the square root of both sides to solve for x.

√((x + 2)^2) = √81

In this step, Tony should have taken the square root of both sides, but he made the mistake of only taking the square root of the right-hand side and neglected to take the square root of the left-hand side correctly.

The correct step should be:

x + 2 = ±9

Step 5: Solve for x.

x + 2 = 9 or x + 2 = -9

Step 6: Subtract 2 from both sides to isolate x.

x = 9 - 2 or x = -9 - 2

This will give the correct solutions:

x = 7 or x = -11

So, the error made by Tony occurred in Step 4 where he only took the square root of the right-hand side and neglected to take the square root of the left-hand side correctly.

Hope this helps!