Question

Question 4 of 10

Solve (x-4)²2 = 5.
OA. x=-4± √5
OB. x=5± √√4
OC. x=9 and x = -1
OD. x=4± √5

Answer 1

Given

`(x-4)^2=5`

Find

Solve the equation

Step-by-step explanation

Here we use the quadratic formula to find the value of x.

first we simplify the given eqaution

`\begin{gathered} (x-4)^2=5 \\ x^2+16-8x=5 \\ x^2-8x+11=0 \end{gathered}`

quadratic formula is given by

`x=(-b\pm√(b^2-4ac))/(2a)`

here we have , a = 1 , b = -8 and c = 11

substitute the values in the formula ,

`\begin{gathered} x=(-(-8)\pm√((-8)^2-4*1*11))/(2*1) \\ \\ x=(8\pm√(64-44))/(2) \\ \\ x=(8\pm√(20))/(2) \\ \\ x=(8\pm2√(5))/(2) \\ \\ x=4\pm√(5) \end{gathered}`

Final Answer

Therefore , the correct option is D.