Question

Tran is solving the quadratic equation 2x2 – 4x – 3 = 0 by completing the square. His first four steps are shown in the table. In which step did Tran first make an error? Step 1 Step 2 Step 3 Step 4Tran is solving the quadratic equation 2x2 – 4x – 3 = 0 by completing the square. His first four steps are shown in the table. In which step did Tran first make an error? Step 1 Step 2 Step 3 Step 4

Answer 1

Tran made his first mistake in this Step 3

Because Tran did not multiply the term 1 by the leading coefficient in the right side

Answer 2

we have

`2x^(2)-4x-3=0`

Step 1

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`2x^(2)-4x=3`

Step 2

Factor the leading coefficient

`2(x^(2)-2x)=3`

Step 3

Complete the square. Remember to balance the equation by adding the same constants to each side

`2(x^(2)-2x+1)=3+2` ------> Tran made his first mistake in this Step 3

Because Tran did not multiply the term 1 by the leading coefficient in the right side

`2(x^(2)-2x+1)=5`

Step 4

Rewrite as perfect squares

`2(x-1)^(2)=5`

therefore

the answer is

Step 3