$x^{2}$ + px +16 = 154

p = ?

asked by guest
on Nov 16, 2024 at 9:53 am



You asked:

Solve the equation \({x}^{2} + p x + 16 = 154\) for the variable \(p\).

MathBot Answer:

The graph of the equation \({x}^{2} + p x + 16 = 154\) is a hyperbola.

The coordinates of its foci are: \(\left(- \frac{\sqrt{\frac{1}{\frac{1}{276} + \frac{\sqrt{2}}{276}} - \frac{1}{\frac{1}{276} - \frac{\sqrt{2}}{276}}}}{\sqrt{2 \sqrt{2} + 4}}, - \frac{\sqrt{2} \sqrt{\frac{1}{\frac{1}{276} + \frac{\sqrt{2}}{276}} - \frac{1}{\frac{1}{276} - \frac{\sqrt{2}}{276}}}}{\sqrt{2 \sqrt{2} + 4}} - \frac{\sqrt{\frac{1}{\frac{1}{276} + \frac{\sqrt{2}}{276}} - \frac{1}{\frac{1}{276} - \frac{\sqrt{2}}{276}}}}{\sqrt{2 \sqrt{2} + 4}}\right)\) and \(\left(\frac{\sqrt{\frac{1}{\frac{1}{276} + \frac{\sqrt{2}}{276}} - \frac{1}{\frac{1}{276} - \frac{\sqrt{2}}{276}}}}{\sqrt{2 \sqrt{2} + 4}}, \frac{\sqrt{\frac{1}{\frac{1}{276} + \frac{\sqrt{2}}{276}} - \frac{1}{\frac{1}{276} - \frac{\sqrt{2}}{276}}}}{\sqrt{2 \sqrt{2} + 4}} + \frac{\sqrt{2} \sqrt{\frac{1}{\frac{1}{276} + \frac{\sqrt{2}}{276}} - \frac{1}{\frac{1}{276} - \frac{\sqrt{2}}{276}}}}{\sqrt{2 \sqrt{2} + 4}}\right)\).

The coordinates of its vertices are: \(\left(- \frac{1}{\sqrt{\frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}}, - \frac{\sqrt{2}}{\sqrt{\frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}} - \frac{1}{\sqrt{\frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}}\right)\) and \(\left(\frac{1}{\sqrt{\frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}}, \frac{1}{\sqrt{\frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}} + \frac{\sqrt{2}}{\sqrt{\frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}}\right)\).

The asymptotes have equations: \(p \left(- \frac{276}{\sqrt{- \frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}} - \frac{276 \sqrt{2}}{\sqrt{\frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}} - \frac{276}{\sqrt{\frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}}\right) + x \left(- \frac{276 \sqrt{2}}{\sqrt{- \frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}} - \frac{276}{\sqrt{- \frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}} + \frac{276}{\sqrt{\frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}}\right) = 0\) and \(p \left(- \frac{276}{\sqrt{- \frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}} + \frac{276}{\sqrt{\frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}} + \frac{276 \sqrt{2}}{\sqrt{\frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}}\right) + x \left(- \frac{276 \sqrt{2}}{\sqrt{- \frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}} - \frac{276}{\sqrt{- \frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}} - \frac{276}{\sqrt{\frac{1}{276} + \frac{\sqrt{2}}{276}} \sqrt{2 \sqrt{2} + 4}}\right) = 0\).

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