Question

Solve (x-4)^2=5

answer: (x=5+√4

Answer 1

Explanation:

Take the square root of each side of the equation to set up the solution for x

`(x-4)^{2*(1)/(2) } =` ±
`√(5)`

Remove the perfect root factor x - 4 under the radical to solve for x.

x - 4 = ±
`√(5)`

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the ± to find the first solution.

`x-4=√(5)`

Add 4 to both sides of the equation.

`x=√(5) +4`

Next, use the negative value of the ± to find the second solution.

`x-4=-√(5)`

Add 4 to both sides of the equation.

`x=-√(5) +4`

The complete solution is the result of both the positive and negative portions of the solution.

`x=√(5) +4,-√(5) +4`

Answer 2

x = 4 + sqrt 5

x = 4 - sqrt 5

Explanation:

(X-4)^2 = 5

X - 4 = + - sqrt 5

X = 4 + sqrt 5 and

X = 4 - sqrt 5