Question

c. 2x² + 15 = -35

Explanation:

Step1: Isolate the quadratic term

Subtract 15 from both sides of the equation $2x^{2}+15 = - 35$.
We get $2x^{2}=-35 - 15$.
Simplifying the right - hand side: $2x^{2}=-50$.

Step2: Solve for $x^{2}$

Divide both sides of the equation $2x^{2}=-50$ by 2.
We have $x^{2}=\frac{-50}{2}=-25$.

Step3: Analyze the solution for $x$

For any real number $x$, the square of $x$, i.e., $x^{2}$, is always non - negative (by the property of real numbers: if $x\in R$, then $x^{2}\geq0$). But here we have $x^{2}=-25$, which is negative. So, there is no real solution for this equation. If we consider complex numbers, we can write $x=\pm\sqrt{-25}=\pm5i$, where $i$ is the imaginary unit with the property $i^{2}=-1$. But if we are restricted to real numbers, the equation has no solution.

Answer:

If we are considering real - valued solutions, the equation $2x^{2}+15=-35$ has no real solution. If we consider complex - valued solutions, $x = \pm5i$.