Question

Help with number 50 please. Thanks.

Answer 1

`d = 7 + 3√(3)` and

`d = 7 - 3√(3)`

Explanation:

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

Recall: quadratic formula =
`(-b ± √(b^2 - 4ac))/(2a)`

Where,

a = 1

b = -14

c = 22

Plug in your values into the formula and solve:

`(-(-14) ± √((-14)^2 - 4(1)(22)))/(2(1))`

`(14 ± √(196 - 88))/(2)`

`(14 ± √(108))/(2)`

`d = (14 + √(108))/(2)`

`d = (14 + 6√(3))/(2)`

`d = ((2(7 + 3√(3)))/(2)`

`d = 7 + 3√(3)`

And

`d = (14 - √(108))/(2)`

`d = (14 - 6√(3))/(2)`

`d = ((2(7 - 3√(3)))/(2)`

`d = 7 - 3√(3)`