Question

16x2-24x-1=0
som
Solve by quadratic equation
using quadratic formula​

Answer 1

Answer:

${16x}^{2} - 24x - 1 = 0$

$d = {b}^{2} - 4ac }$

$( - 24)}^{2} - 4(16)( - 1) }$

${576 + 64}$

$640$

$x = \frac{ - b + - \sqrt{d} }{2a}$

$x = \frac{ - ( - 24) + - \sqrt{640} }{2 \times 16}$

$x = \frac{24 + - 8\sqrt{10} }{32}$

$( + ) \alpha = \frac{24 + 8 \sqrt{10} }{32}$

$\alpha = \frac{8(3 + \sqrt{10)}}{32}$

$\alpha = \frac{3 + \sqrt{10} }{4}$

$( - )\beta = \frac{24 - 8 \sqrt{10}}{32}$

$\beta = \frac{8(3 - \sqrt{10)} }{32}$

$\beta = \frac{3 - \sqrt{10} }{4}$

Answer 2

$x \: = - b + - \frac{ \sqrt{ {b}^{2} - 4ac } }{2a}$

$x = - ( - 24) + - \frac{ \sqrt{ {(24)}^{2} - 4 \times 16 \times ( - 1)} }{2 \times 16} \\ x = 24 + - \frac{ \sqrt{576 + 64} }{32} \\ x = 24 + - \frac{ \sqrt{640} }{32} \\ x = 24 + - \frac{ 8 \sqrt{10} }{32} \\ x = \frac{24}{32} + \frac{ 8\sqrt{10} }{32} \: \: \: \: \: \: \: \: \: \: \: \:or \: \: \: \: \: \: x = \frac{24}{32} - \frac{ 8 \sqrt{10} }{32} \\ x = \frac{24}{32} + \frac{ 8\sqrt{10} }{32} \:\:\: or \:\:\:\: x = \frac{24}{32} - \frac{ 8\sqrt{10} }{32} \\ x = \frac{ 3 + \sqrt{10} }{4} \: \: \: \: \: \: or \: \: \: \: \: \: \: \: x = \frac{ 3 - \sqrt{10} }{4}$