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Complete the square to solve the equation below.

x2 - 10x - 2 = 17

A. x = 5 + ; x = 5 -
B. x = 5 + ; x = 5 -
C. x = 5 + ; x = 5 -
D. x = 6 + ; x = 6 -

Respuesta :

BlueSky06
We need to solve for the values of x by applying the method of completing the square in the given expression x² - 10x -2 = 17. The solution is shown below:
x² - 10x -2 = 17
Transpose -2 to the right side such as:
x² - 10x = 17 + 2
Perform addition of 17 and 2
x² - 10x = 19
Add + 25 in both sides
x² - 10x + 25 = 19 + 25
x² - 10x + 25 = 44
(x-5)(x-5) = 44
Where (x-5) is a perfect square, then we have:
(x-5)² = 44
x1 = +√44 -5 = 1.6
x2 = - √44 -5 = -11.6

The answers are x1=1.6 and x2 = -11.6.

Answer:

Option A and B  [tex](x-5)^2-44=0[/tex]

Step-by-step explanation:

We have given that : [tex]x^2 - 10x - 2 = 17[/tex]

Applying completing the square

Step 1 :  [tex]x^2 - 10x - 2 = 17[/tex] (write the equation)

Step 2:  [tex]x^2 - 10x = 17+2[/tex]

Step 3: [tex]x^2 - 10x +25 =19+25[/tex] (add 25 both side)

Step 4:  [tex](x-5)^2=44[/tex]

Step 5: [tex](x-5)^2-44=0[/tex]

Square to solve the equation is A and B as both are same.

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