40. Solve $$ 49-4 x^{2}=625 $$. (A) $$ x=-12 $$ (B) $$ x=12 $$ (C) $$ x= \pm 12 i $$ (D) $$ x=12 i $$

Question

UpStudy AI · Accepted Answer

To solve the equation $$ 49 - 4x^{2} = 625 $$, follow these steps:

1. **Isolate the $$ x^2 $$ term:**

$$
   49 - 4x^{2} = 625 \
   -4x^{2} = 625 - 49 \
   -4x^{2} = 576
   $$

2. **Solve for $$ x^2 $$:**

$$
   x^{2} = \frac{576}{-4} \
   x^{2} = -144
   $$

3. **Take the square root of both sides:**

$$
   x = \pm \sqrt{-144} \
   x = \pm 12i
   $$

Here, $$ i $$ is the imaginary unit, defined as $$ i = \sqrt{-1} $$.

So, the solutions are $$ x = 12i $$ and $$ x = -12i $$.

**Answer:** (C) $$ x= \pm 12 i $$
The solutions are $$ x = 12i $$ and $$ x = -12i $$.

Solve .
(A)
(B)
©
(D)