Question

Help with number 50 please. Thanks.

Answer 1

Answer:

$d = 7 + 3\sqrt{3}$ and

$d = 7 - 3\sqrt{3}$

Step-by-step explanation:

To solve the equation, $d^2 - 14d - 22 = 0$, using the quadratic formula,

Recall: quadratic formula = $\frac{-b ± \sqrt{b^2 - 4ac}}{2a}$

Where,

a = 1

b = -14

c = 22

Plug in your values into the formula and solve:

$\frac{-(-14) ± \sqrt{(-14)^2 - 4(1)(22)}}{2(1)}$

$\frac{14 ± \sqrt{196 - 88}}{2}$

$\frac{14 ± \sqrt{108}}{2}$

$d = \frac{14 + \sqrt{108}}{2}$

$d = \frac{14 + 6\sqrt{3}}{2}$

$d = (\frac{2(7 + 3\sqrt{3})}{2}$

$d = 7 + 3\sqrt{3}$

And

$d = \frac{14 - \sqrt{108}}{2}$

$d = \frac{14 - 6\sqrt{3}}{2}$

$d = (\frac{2(7 - 3\sqrt{3})}{2}$

$d = 7 - 3\sqrt{3}$