Question

Solve the quadratic equation.

x^2 – 10x + 25 = 0
A. x = 5 or -5
B. x = 5
C. x = -5
D. no real solution

Answer 1

I think the answer is x=5

Answer 2

x = 5

which agrees with option B) among the list of answers

Explanation:

We can solve by grouping or by recognizing the general form of a perfect square binomial.

By grouping we use that -10x can be written as :

-5x -5x

and substitute the middle term with this expression and then factoring by grouping:

x^2 - 5 x - 5 x +25 = 0

[x^2- 5 x] + [ -5 x + 25] = 0

x [ x - 5] - [5 x - 25] = 0

x [x - 5] - 5 [x - 5] = 0

[x - 5] (x - 5) = 0

Which is a factor form that has a unique solution

x = 5

So we opt for option B) in the list of possible answers.