Question

Amelie found the solutions of the equation x^2-x=42 to be 6 and -7. Explain why this answer is incorrect. Then, find the correct solutions.

Answer 1

see below

Explanation:

x^2-x=42

Check the solutions

6^2 -6 = 42

36-6 =42

30=42

This is not true so 6 is not a solution

Let's find the solutions

Subtract 42 from each side

x^2-x-42=0

Factor

(x-7)(x+6) =0

Using the zero product property

x-7 =0 x+6=0

x=7 x=-6