Question

In simplest radical form, what are the solutions to the quadratic equation 6 = x2 - 10/?

Quadratic formula: * = -bt/b? 40c
20
O x=5+31
O x = 51/19
O x = 5+219
O x = 5+2/31

Answer 1

`x = 5 \± √(31)`

Explanation:

Given

`6 = x^2 - 10x`

Required

The solution in radical form

`6 = x^2 - 10x`

Rewrite as:

`x^2 - 10x - 6 = 0`

Using the quadratic formula, we have:

`x = (-b \± √(b^2 - 4ac))/(2a)`

Where

a = 1

b = -10

c = -6

So, we have:

`x = (-(-10) \± √((-10)^2 - 4*1*(-6)))/(2*1)`

`x = (10 \± √(100 +24))/(2*1)`

`x = (10 \± √(124))/(2)`

Split the roots

`x = (10 \± √(4 * 31))/(2)`

Express
`\sqrt 4` as 2

`x = (10 \± 2√(31))/(2)`

Split the fraction

`x = (10)/(2) \± (2√(31))/(2)`

`x = 5 \± √(31)`