1. **Problem:** Find the values of $x$ and $y$ given the equations: $$x^2 = 7t$$ $$= iy + 20i - 12$$ 2. **Step 1: Understand the problem** We have two expressions involving $x$, $y$, and $t$. The first is $x^2 = 7t$. The second expression is ambiguous but appears to be an equation involving imaginary unit $i$, $y$, and constants: $= iy + 20i - 12$. We interpret this as an equation to solve for $y$. 3. **Step 2: Solve for $x$ in terms of $t$** From the first equation: $$x^2 = 7t$$ Taking square root on both sides: $$x = \pm \sqrt{7t}$$ 4. **Step 3: Solve for $y$ from the second equation** Assuming the second equation is: $$z = iy + 20i - 12$$ If $z$ is a complex number, equate real and imaginary parts: Real part: $-12$ Imaginary part: $iy + 20i = i(y + 20)$ If the left side is purely imaginary or real, we can isolate $y$ accordingly. Without more context, we isolate $y$: $$iy + 20i - 12 = 0$$ Rearranged: $$iy + 20i = 12$$ Divide both sides by $i$: $$y + 20 = \frac{12}{i} = -12i$$ So: $$y = -12i - 20$$ 5. **Final answers:** $$x = \pm \sqrt{7t}$$ $$y = -20 - 12i$$ This completes the solution for the first problem.