Question

Find all real solutions of the equation by completing the square. (Enter your answers as a comma-separated list.) x2 − 4x − 8 = 0

Answer 1

Answer:

After completing the square the expression is (x-2)^2 -12 =0 and real solution are x = 5.46 and x = -1.46

Step-by-step explanation:

We need to complete the square:

x^2 − 4x − 8 = 0

x^2 -2(x)(2)+(2)^2 -8 -4 =0

(x^2 -4x +4) - 12 = 0

(x-2)^2 -12 =0

Now, finding the value of x

(x-2)^2 -12 =0

(x-2)^2 = 12

taking square root on both sides

$\sqrt{(x-2)^2}= \sqrt{12} \\(x-2) = \pm\sqrt{12} \\x = \pm\sqrt{12} +2\\x = \sqrt{12}+2 \,\,and\,\,x=-\sqrt{12}+2\\x= 3.46+2 \,\,and\,\,x=-3.46+2\\x =5.46\,\,and\,\,x=-1.46$

So, After completing the square the expression is (x-2)^2 -12 =0 and real solution are x = 5.46 and x = -1.46