Question

Solve the quadratic equation by completing the square. x^2+14x+47=0. What is the form and solution?

Answer 1

To complete a square for ax²+bx+c, you first make a=1.
in this case, a is already 1
move c to the right side: x²+14x=-47
next, add (1/2 of b)² to both sides, in this case, b=14, half of 14 is 7, so x²+14x+ 7²=-47+7²
the left side is now a perfect square: (x+7)²=2
x+7=√2 or x+7=-√2
x=√2-7, or x=-2-√7