Completing The Square To Solve A Quadratic Equation

Ordinarily we try to factor a quadratic expression and solve for two roots by using either the zerios of the expression or the quadratic formula, which is derived from the process of completing the square.  We may also complete the square to solve the equation if we cannot factor upon inspection.

Example:

x² + 8x + 2=0 may not be factored upon inspection.

We move the constant to the right side of the equation, which now appears as:

x2 +8x = -2

We then take half the coefficient of the x term, or 4, and square it, adding it to both sides of the equaion:

x² + 8x + 16= -2+16= 14

Since we now have a perfectly expanded square on the left side, we may express it as:

(x+4)²=14

If we take the square root of both side of the equation, we  find that

x+4= +14, -14
and
x= +14 -4. -14 -4