consider the following quadratic equation x^(2)-10x+25=0 using the standard form ax^(2)+bx+c=0 of the given quadratic equation factor the left hand side of the equation into two linear factors
To factorize the quadratic equation x^2 - 10x + 25 = 0, we can use the formula for finding the roots of a quadratic equation:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = -10, and c = 25. Plugging these values into the formula, we have:
x = (-(-10) ± √((-10)^2 - 4(1)(25))) / (2(1))
x = (10 ± √(100 - 100)) / 2
x = (10 ± √0) / 2
x = (10 ± 0) / 2
Since the square root of 0 is 0, we have:
x = (10 + 0) / 2 = 10 / 2 = 5
x = (10 - 0) / 2 = 10 / 2 = 5
Thus, the equation x^2 - 10x + 25 = 0 can be factored into:
(x - 5)(x - 5) = 0
Therefore, the left-hand side of the equation can be factored into two linear factors as (x - 5)(x - 5).