Final answer:
To express x - 10x¹/² + 25 = 0 in quadratic form, substitute t for √{x}, yielding t² - 10t + 25 = 0. This is a quadratic equation and can be factored to (t - 5)² = 0, implying that x = 25.
Step-by-step explanation:
To express the equation x - 10x¹/² + 25 = 0 in quadratic form, we can recognize that it is already in the form of a quadratic equation when we identify that 10x¹/² is actually 10√{x} which can be rewritten as 10x¹/². Therefore, we can let t be x¹/² (or √{x}), which implies that t² = x. Substituting this back into the original equation, we can rewrite it as t² - 10t + 25 = 0, which is now clearly in the form of at² + bt + c = 0 with a = 1, b = -10, and c = 25.
This equation is factorable as
(t - 5)² = 0
, which means that
t = 5
. Since
t = √{x}
, this gives us
√{x} = 5
or
x = 25.
Using the quadratic formula is unnecessary here because the equation is already factorable, but for general cases of quadratic equations, the formula x = (-b ± √{b² - 4ac})/(2a) can be used to find the solutions for x.