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

Answer:

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

Step-by-step 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:

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

Answer 2

Answer:

Eliza could have written √(z + 3)² = √20 in Step 2

Step-by-step explanation:

For step 2, we have

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

However, Eliza could have written from (z + 3)² - 2 = 18,

Step 1 (z + 3)² = 18 + 2 = 20

Adding  2 to both sides

Step 2: √(z + 3)² = √20

Finding the square root of both sides

Step 3: z + 3 = √20

Rationalizing the left hand side of the equation

Step 4: √20 - 3

Subtracting 3 from both sides

Therefore, the step missing in step 2 was the finding of the square root of both sides of the equation

Which was taken as the division of both sides by 2.