K2-4K-10=4

Question

solve each equation by completing the square?

 

Answer 1

k² - 4k - 10 = 4

 

 

When completing the square, we want the quadratic factor to be a perfect trinomial.  If we add 14 to both sides of the equation, we get

 

k² - 4k - 10 + 14 = 4 + 14

 

k² - 4k + 4 = 18

 

(k - 2)(k - 2) = 18

 

(k - 2)² = 18

 

 

Square-root both sides of the equation to undo the exponent on the left side.

 

k - 2 = ±√18

 

k = 2 ± √18

 

 

Break down the radical term.

 

k = 2 ± 3√2

 

Answer 2

k² - 4k -10 = 4

 

k² -4k   = 14

 

k² -4x + 4 = 14 + 4

 

(k-2)² = 18

 

k = 2 +/- sqrt(18)  = 2 +/ 3sqrt(2)