Question

Solve the quadratic equation by completing the square. x^2-14x+42=0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas.

Form: ______
Solution: _______

Answer 1

x^2-14x+42=0 subtract 42 from both sides

x^2-14x=-42 halve the linear coefficient, square it, add it to both sides, in this case: (14/2)^2=7^2=49, add 49 to both sides

x^2-14x+49=7 now the left side is a perfect square...

(x-7)^2=7 take the square root of both sides

x-7=±√7 add 7 to both sides

x=7±√7

The above is the two solutions, 7+√7 and 7-√7

I am not sure what they mean by the proper form other than perhaps the point when you have a complete square as in the point in the process where you have a perfect square...

(x-7)^2=7

Answer 2

x^2 - 14x + 42 = 0
x^2 - 14x = -42
x^2 - 14x + 49 = 49 - 42
(x - 7)^2 = 7
x - 7 = (+-) sqrt 7
x = 7 (+-) sqrt 7

solutions are : x = 7 + sqrt 7 and x = 7 - sqrt 7