Question

susu is solving the quadratic equation (4x^2 - 8x - 13 = 0) by completing the square.
susu’s work

	(4x^2 - 8x - 13 = 0)
step 1	(4x^2 - 8x = 13)
step 2	(4(x^2 - 8x) = 13)
step 3	(4(x^2 - 8x + 16) = 13 + 64)
step 4	(4(x - 4)^2 = 77)

in which step did susu first make an error?
step 4
step 2
step 1
step 3

Explanation:

Step1: Analyze Step 1

The original equation is \(4x^{2}-8x - 13=0\). Moving \(- 13\) to the right side gives \(4x^{2}-8x=13\). Step 1 is correct.

Step2: Analyze Step 2

To factor out the coefficient of \(x^{2}\) from the left - hand side, we have \(4x^{2}-8x = 4(x^{2}-2x)\) (since \(4x^{2}\div4=x^{2}\) and \(-8x\div4=-2x\)), but Susu wrote \(4(x^{2}-8x)\), which is wrong. So we can see that the first error occurs in Step 2.

Step3: (Optional, for completeness) Analyze Step 3 and Step 4

Even though we already found the error in Step 2, for completeness:

• In Step 3, if we follow the wrong Step 2, when completing the square inside the parentheses \(x^{2}-8x\), we take half of \(-8\) which is \(-4\), square it to get \(16\). But since there is a factor of \(4\) outside the parentheses, adding \(16\) inside the parentheses is equivalent to adding \(4\times16 = 64\) to the left - hand side. So we should add \(64\) to the right - hand side. But since Step 2 is already wrong, the error in Step 3 is a consequence of Step 2's error.
• Step 4 is also wrong because of the previous errors, but the first error is in Step 2.

Answer:

Step 2