Solve the quadratic equation.
x^2 − 10x + 25 = 0
a. x = 5 or −5
b. x = 5
c. x = −5
d. no real solution
To solve the quadratic equation x^2 − 10x + 25 = 0, we can try factoring or using the quadratic formula.
Factoring:
x^2 − 10x + 25 = 0
(x - 5)(x - 5) = 0
(x - 5)^2 = 0
x - 5 = 0
x = 5
Using the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac))/(2a)
For the equation x^2 − 10x + 25 = 0, we have a = 1, b = -10, and c = 25.
Plugging these values into the quadratic formula:
x = (-(-10) ± √((-10)^2 - 4(1)(25)))/(2(1))
x = (10 ± √(100 - 100))/(2)
x = (10 ± √0)/(2)
x = (10 ± 0)/(2)
x = 10/2
x = 5
Therefore, the solution to the quadratic equation x^2 − 10x + 25 = 0 is x = 5.
The answer is b. x = 5.