Question

Rewrite the following in a 6th graders response

The error in George's solution is that he factored the quadratic expression without setting the equation to zero first.
In Step 2, he incorrectly assumes that if
(x+5)(x-1) = 7, then x + 5= 0
and x - 1 = 0. This is only true when
the quadratic expression is equal to zero.
To correctly solve the equation, George should have first subtracted 7 from both sides of the equation to get
x^2+ 4x - 12 = 0. Then, he could have
factored the quadratic expression as
(x + 6) (x - 2) = 0, and set each factor
equal to zero to find the solutions
x=-6 and x = 2

Answer 1

George made a mistake because he factored the expression before making the equation equal to zero.

What he did wrong:
- He thought (x + 5)(x - 1) = 7 means x + 5 = 0 or x - 1 = 0. That only works when the product equals 0, not 7.

Correct way to solve it:
1. Subtract 7 from both sides: (x + 5)(x - 1) − 7 = 0.
2. Expand and simplify: x^2 + 4x − 12 = 0.
3. Factor: (x + 6)(x − 2) = 0.
4. Set each factor to zero: x + 6 = 0 → x = −6, and x − 2 = 0 → x = 2.

Check:
- For x = 2: (2 + 5)(2 − 1) = 7·1 = 7 ✓
- For x = −6: (−6 + 5)(−6 − 1) = (−1)(−7) = 7 ✓

So the answers are x = −6 and x = 2.