Solve the following quadratic equations using completing the square x2 - 8x - 34 = 0

4 + 5sqrt (2), 4 - 5sqrt (2)

Step-by-step explanation:

x² - 8x - 34 = 0

x = [ - (-8) + / - sqrt ((-8) ² - 4 (1) (-34)) ]/2

x = (8 + / - sqrt200) / 2

x = 4 + / - 5sqrt (2)

x=4± 5sqrt (2)

Step-by-step explanation:

x^2 - 8x - 34 = 0

To complete the square Add 34 to each side

x^2 - 8x - 34+34=0 + 34

Take the coefficient of x, and divide by 2

-8/2 = -4

Then square it and add it to each side

(-4) ^2 = 16

x^2 - 8x + 16 = 34+16

x^2 - 8x + 16 = 50

We replace the left side with (x + the coefficient of x/2) ^2

(x - 4) ^2=50

Take the square root of each side

sqrt ((x - 4) ^2) = ±sqrt (50)

x-4 = ±sqrt (25*2)

x-4 = ±sqrt (25) * sqrt (2)

x-4 = ±5sqrt (2)

Add 4 to each side

x=4± 5sqrt (2)