Solve: $$ -7 x^{2}+10=185 $$ $$ x=3,-3 $$ $$ x=5,-5 $$ $$ x=3 $$ I'm not sure.

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UpStudy AI · Accepted Answer

**Step 1: Write the equation**

$$
-7x^{2} + 10 = 185
$$

**Step 2: Isolate the quadratic term**

Subtract $$10$$ from both sides:

$$
-7x^{2} = 185 - 10 = 175
$$

**Step 3: Solve for $$x^2$$**

Divide both sides by $$-7$$:

$$
x^{2} = \frac{175}{-7} = -25
$$

**Step 4: Analyze the result**

The equation $$x^{2} = -25$$ implies that:

$$
x = \pm \sqrt{-25}
$$

Since the square root of a negative number introduces the imaginary unit $$i$$, we have:

$$
x = \pm 5i
$$

**Conclusion**

There are no real solutions for the equation. The solutions in the complex number system are:

$$
x = 5i \quad \text{and} \quad x = -5i
$$
The equation has no real solutions. In the complex number system, the solutions are $$ x = 5i $$ and $$ x = -5i $$.

Solve:

I’m not sure.

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