Question

given:
$x + 3 = \sqrt{36x^2}$
step 1
$(x + 3)^2 = \left(\sqrt{36x^2}\
ight)^2$
step 2:
$x^2 + 6x + 9 = \left(\sqrt{36x^2}\
ight)^2$
step 3
$x^2 + 6x + 9 = 6x$
step 4
$x^2 + 9 = 0$
step 5
$x^2 = -9$
step 6
$x = \pm 3i$
the image shows a work done to solve a radical equation. between which two steps is the error made
options:
no error made
step 1 and step 2
given and step 1
step 2 and step3

Explanation:

Step1: Simplify the radical term

$\sqrt{36x^2} = |6x| = 6|x|$, so $(\sqrt{36x^2})^2 = (6|x|)^2 = 36x^2$

Step2: Compare Step 2 and Step3

Step 2 gives $x^2 + 6x + 9 = (\sqrt{36x^2})^2$, which should equal $36x^2$, but Step3 incorrectly writes it as $6x$.

Answer:

D. Step 2 and Step3