Find an equation that has the given solutions: $x=\frac{-1\pm 5i}{2}$
Write your answer in standard form.

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Step 1 ：The given solutions are complex numbers. The solutions of a quadratic equation are given by the formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$. Comparing this with the given solutions, we can see that $b=1$, $a=2$ and the discriminant $b^2-4ac$ is $-25$. We can use these values to find the coefficients of the quadratic equation.

Step 2 ：Let's denote the solutions as $x1=(-0.5+2.5j)$ and $x2=(-0.5-2.5j)$.

Step 3 ：From the quadratic formula, we can set up the following system of equations: $2\ast a=1$ (eq1), $b=-1$ (eq2), and $-4\ast a\ast c+b^2=-100.0$ (eq3).

Step 4 ：Solving this system of equations gives the coefficients of the quadratic equation. The coefficient $a$ is $0.5$, $b$ is $-1$, and $c$ is $50.5$.

Step 5 ：Therefore, the quadratic equation that has the given solutions is $0.5x^2-x+50.5=0$.

Step 6 ：Final Answer: The quadratic equation that has the given solutions is $\boxed{{\displaystyle 0.5x^2-x+50.5=0}}$.