Problem

Francisco claimed that the equation $x^{2}-8 x=0$ cannot be solved by the quadratic formula since there is no value for $\mathrm{c}$. Is he correct?

Answer

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Answer

\(\boxed{\text{Final Answer: Francisco's claim is incorrect. The equation } x^{2}-8 x=0 \text{ can be solved by the quadratic formula, even when } c=0. \text{ The solutions are } x=0 \text{ and } x=8.}\)

Steps

Step 1 :Francisco claimed that the equation \(x^{2}-8 x=0\) cannot be solved by the quadratic formula since there is no value for \(c\). Is he correct?

Step 2 :The quadratic formula is used to solve equations of the form \(ax^2 + bx + c = 0\). In this case, the equation is \(x^2 - 8x = 0\), which can be rewritten as \(x^2 - 8x + 0 = 0\). So, the value of \(c\) is 0.

Step 3 :Francisco's claim that the equation cannot be solved by the quadratic formula because there is no value for \(c\) is incorrect. The quadratic formula can still be used even if \(c\) is 0.

Step 4 :The solutions to the equation \(x^{2}-8 x=0\) are \(x=0\) and \(x=8\). These solutions confirm that the quadratic formula can be used to solve the equation, even when \(c=0\).

Step 5 :\(\boxed{\text{Final Answer: Francisco's claim is incorrect. The equation } x^{2}-8 x=0 \text{ can be solved by the quadratic formula, even when } c=0. \text{ The solutions are } x=0 \text{ and } x=8.}\)

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