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Finding Constant c for One Real Solution in Quadratics

Very Hard Advanced Math Quadratic Equations

Consider the quadratic equation given by:

$$2x^2 - 8x + c = 0$$

where $c$ is a real number constant. For the equation to have exactly one real solution, the discriminant must be equal to zero. Recall that the discriminant $D$ for a quadratic equation $ax^2 + bx + c = 0$ is given by:

$$D = b^2 - 4ac$$

Using this information, determine the value of $c$ that ensures the equation has exactly one real solution, and provide your answer in both fractional and decimal forms.

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