Answer:
x=5+5√2; x=5-5√2
Step-by-step explanation:
To complete the square we need to turn part of the equation into a perfect square trinomial. Remember, in any equation we can do anything we like to the numbers as long as both sides stay equal.
First, let's subtract 10 from both sides.
x^2-10x=25
This does not factor, so we need to turn it into a perfect square trinomial by adding the quantity equal to (b/2)^2. In this case, (b/2)^2 is 25.
x^2−10x+25=25+25
IMPORTANT: You must keep the sides of the equation equal, so we added a 25 to the right side as well to keep the equation true.
From here we can factor, simplify and find our zeroes.
(x-5)(x-5)=50
(x-5)^2=50
x-5=±√50
x=5±√50
√50=5√2
So our final answer is:
x=5+5√2; x=5-5√2
HTH :)
