Question

7x^2-20x+14=0 через k

Answer 1

A=7, b=-20, k=-10, c=14
D1=k^2-ac=100-7*14=2, √2
x1=(10-√2)/7
x2=(10+√2)/7

Answer 2

To solve the quadratic equation 7x^2 - 20x + 14 = 0 by completing the square, we can first divide both sides by 7 to get:

x^2 - (20/7)x + 2 = 0

Next, we can add and subtract the square of half of the coefficient of x, which is ((20/7)/2)^2 = (5/7)^2 = 25/49:

x^2 - (20/7)x + 25/49 - 25/49 + 2 = 0

Now we can simplify the expression inside the parentheses:

(x - 5/7)^2 - 11/49 = 0

Finally, we can add 11/49 to both sides and take the square root:

(x - 5/7)^2 = 11/49

x - 5/7 = ±sqrt(11)/7

x = 5/7 ±sqrt(11)/7

Therefore, the solutions to the equation 7x^2 - 20x + 14 = 0 can be expressed in terms of k as:

x = 5/7 + ksqrt(11)/7 or x = 5/7 - ksqrt(11)/7