ExpandProcessLog\( \mathrm { 12 \cdot \left(-4\right) = -48 } \)Str\( \mathrm { p^{2} - 48 = 4 } \)\( \mathrm { p^{2} + 12 \cdot \left(-4\right) = 4 } \)\( \mathrm { p^{2} - 48 = 4 } \)SimplifyExpandStr\( \mathrm { p^{2} - 48 = 4 } \)ExpandProcessLog\( \mathrm { -48 - 4 = -52 } \)Str\( \mathrm { p^{2} - 52 = 0 } \)ProcessLogDetermine the discriminant of the quadratic equation to find the roots : \n \( \mathrm { a x ^ { 2 } + b x + c \Longrightarrow \Delta = b ^ { 2 } - 4 a c } \) \n \( \mathrm { a = 1 } \) \n \( \mathrm { b = 0 } \) \n \( \mathrm { c = -52 } \)Str\( \mathrm { \Delta = 0^{2} + \left(-4\right) \cdot \left(-52\right) } \)ProcessLogSimplify the exponents: \n \( \mathrm { 0^{2} = 0 } \)Str\( \mathrm { \Delta = \left(-4\right) \cdot \left(-52\right) } \)ProcessLog\( \mathrm { \left(-4\right) \cdot \left(-52\right) = 208 } \)Str\( \mathrm { \Delta = 208 } \)ProcessLogSince discriminant greater than zero the equation has two distinct real roots. Use the quadratic formula \( \mathrm { x _{ 1, 2 } = \displaystyle\frac { - b \pm \sqrt { \Delta } } { 2 a } } \) to determine roots.StrFirst root: \( \mathrm { p_{1} = \displaystyle\frac{0 + \sqrt{208}}{2} } \)ExpandProcessLogSimplify the root: \n \( \mathrm { \sqrt{208} = 4 \cdot \sqrt{13} } \)Str\( \mathrm { p_{1} = \displaystyle\frac{0 + 4 \cdot \sqrt{13}}{2} } \)ProcessLogSimplify the numerator and denominator: \n \( \mathrm { \displaystyle\frac{2 \cdot 2}{2} = 2 } \)Str\( \mathrm { p_{1} = 2 \cdot \sqrt{13} } \)\( \mathrm { p_{1} = \displaystyle\frac{0 + \sqrt{208}}{2} } \)\( \mathrm { p_{1} = 2 \cdot \sqrt{13} } \)SimplifyStrSecond root: \( \mathrm { p_{2} = \displaystyle\frac{0 - \sqrt{208}}{2} } \)ExpandProcessLogSimplify the root: \n \( \mathrm { \sqrt{208} = 4 \cdot \sqrt{13} } \)Str\( \mathrm { p_{2} = \displaystyle\frac{0 - 4 \cdot \sqrt{13}}{2} } \)ProcessLogSimplify the numerator and denominator: \n \( \mathrm { \displaystyle\frac{\left(-2\right) \cdot 2}{2} = -2 } \)Str\( \mathrm { p_{2} = - 2 \cdot \sqrt{13} } \)\( \mathrm { p_{2} = \displaystyle\frac{0 - \sqrt{208}}{2} } \)\( \mathrm { p_{2} = - 2 \cdot \sqrt{13} } \)Simplify\( \mathrm { p^{2} - 52 = 0 } \)\( \mathrm { p = \left\{- 2 \cdot \sqrt{13}, 2 \cdot \sqrt{13}\right\} } \)Determine the roots\( \mathrm { p = \left\{- 2 \cdot \sqrt{13}, 2 \cdot \sqrt{13}\right\} } \)Isolate \( \mathrm { p } \)

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