I'm going to take you through three steps on how to solve this!
1. Quadratic Formula
The quadratic formula, x=−b±√b2−4ac2a is a very neat formula on how to find the roots! Plugging the values into the equation, we yield x1,2=−(−10)±√(−10)2−4⋅1⋅252⋅1 . Solving and doing all the calculations, we get −(−10)2⋅1=5, and that is our only solution!
2. Factoring
We can factor x2−10x+25=0 into (x−5)2 , after trying! Now, set x−5=0 , and our only solution is 5.
3. Completing the Square
To complete the square, we first subtract 25 from both sides, leaving us with x2−10x=−25. Our goal is to write it in the form x2+2ax+a2=(x+a)2 , so we solve for a , which is −5. We add this to get x2−10x+(−5)2=−25+(−5)2 . Solving, we get , (x−5)2=0
and our answer is x=5.
Too many steps! The answer is (B).