Question

Find the error in each of the following solutions. Explain your reasoning
2𝑥^2 − 12𝑥 − 21 = 0
𝑥^2 − 6𝑥 =21/2
𝑥^2 − 6𝑥 + 9 =21/2− 9
(𝑥 − 3)^2 =3/2
𝑥 − 3 = ±√3/2
𝑥 − 3 = ±√3/√2
𝑥 = 3 ±√6/2

Answer 1

The error in each of the following solutions is the incorrect simplification of the equations or expressions.

1. The error is in simplifying 𝑥^2 − 6𝑥 as 21/2. This is incorrect because 21/2 is not the simplified form of 𝑥^2 − 6𝑥. The correct simplification is 𝑥^2 − 6𝑥 - 21 = 0.

2. The error is in subtracting 9 from 21/2 without simplifying the right side of the equation. The correct simplification should be 𝑥^2 − 6𝑥 + 9 = 21/2 - 9/1.

3. The error is in not simplifying the right side of the equation. The correct equation should be (𝑥 − 3)^2 = (3/2) * (2/2).

4. The error is in taking the square root of 3/2 without dividing the square root of 3 and 2. The correct equation should be 𝑥 − 3 = ±√(3/2).

5. The error is in incorrectly dividing the square root of 3 by the square root of 2. The correct equation should be 𝑥 − 3 = ±√(3/√2).

6. The error is in not simplifying the expression correctly. The correct equation should be 𝑥 = 3 ± (√6/2).