Solve the following quadratic equation by completing the square. Simplify the solutions and rationalize denominators, if necessary.

Question

x2 + 6x − 17 = 0

Answer 1

x^2 + 6x - 17 = 0

First separate x terms

X^2 + 6x = 17
or

17 = x^2 + 6x

remember that aX^2 + bx + c
to complete square, divide b by two, and square it.

6/2 = 3.
3^2 = 9.

Now add 9 to each side of the equation

17+9 = x^2 + 6x + 9

combine like terms:
26 = x^2 + 6x + 9

Now factor the right side:
26 = (x+3)(x+3)
26 = (x+3)^2

Now square root the right and left side to get rid of the square:
+,-sqroot(26) = x+3

Your remaining solutions are:
x = -3 +sqr(26)
x = -3 -sqr(26)

note: please recheck into equation, they might not be correct!