Question

Complete the square for 2x^2 - 4x = 14

Answer 1

To complete the square for the equation \(2x^2 - 4x = 14\), follow these steps:

1. **Move the constant to the other side**:
\[
2x^2 - 4x - 14 = 0
\]

2. **Factor out the coefficient of \(x^2\)** (which is 2 in this case) from the terms on the left side:
\[
2(x^2 - 2x) = 14
\]

3. **Divide both sides by 2** to simplify:
\[
x^2 - 2x = 7
\]

4. **Complete the square** for the expression \(x^2 - 2x\):
- Take half of the coefficient of \(x\), which is \(-2\), giving \(-1\).
- Square this value: \((-1)^2 = 1\).
- Add and subtract this square inside the equation:
\[
x^2 - 2x + 1 - 1 = 7
\]
or
\[
(x^2 - 2x + 1) - 1 = 7
\]

5. **Rewrite the left side as a square**:
\[
(x - 1)^2 - 1 = 7
\]

6. **Add 1 to both sides**:
\[
(x - 1)^2 = 8
\]

Now the equation is in completed square form:
\[
(x - 1)^2 = 8
\]