College algebra 1

Question

Solve the quadratic equation by completing the square.

x^2- 6x -5=0

Choose the correct form and fill in the blanks with the correct numbers .

Form:

(x + )^2 =

(x - )^2 =

and solve the equation

x=

Answer 1

A=1, as it should

B = -6

x^2 - 6x - 5 = 0

x^2 - 6x = 5

(B/2)^2 = (-6/2)^2 = (-3)^2 = 9

x^2 - 6x + 9 = 5+9

(x - 3)(x - 3) = 14

(x - 3)^2 = 14

x - 3 = +or- sqrt(14)

x = 3 +or- sqrt(14)

check:

x = 3 + sqrt(14)

x^2 = x*x = (3 + sqrt(14))(3 + sqrt(14))

= 9 + 6*sqrt(14) + 14

= 23 + 6 *sqrt(14)

x^2 - 6x - 5 =

23 + 6 * sqrt(13) - 6( 3 + sqrt(14)) - 5 =

23 + 6 * sqrt(13) - 18 - 6*sqrt(14) - 5 =

23 - 18 - 5 =

5-5=

0