Question

Eliza solved a quadratic equation. Her work is shown below, with Step 2 missing.

What could Eliza have written as the result from Step 2?
(2 + 3)2 – 2 = 18
${z + 3)= 20
Step 1
Step 2
2 + 3 = 10
Step 3
I= -13 or 2 = 7 Step 4

Answer 1

Step 2: (z+3)=20/2

Explanation:

Given Eliza's Work:

`(z + 3)^2$ - 2 = 18\\Step 1:(z + 3)^2= 20\\$Step 2:\\Step 3: z + 3 = 10\\Step 4: z = -13 or z = 7`

For Eliza to have obtained z+3 = 10 in step 3, she erroneously divided the right hand side of step 1 by 2. Therefore, what she wrote in her step 2

Step 2: (z+3)=20/2

However, the correct solution is:

`(z + 3)^2$ - 2 = 18\\Step 1:(z + 3)^2= 20\\$Step 2:√((z + 3)^2) =\pm √(20) \\$Step 3: z + 3 = \pm 2√(5) \\$Step 4: z = -3+ 2√(5)$ or z = -3 - 2√(5)`