CPM Homework Help : INT2 Problem 12-70

Solve the equation below by completing the square. Give your answer(s) in exact (radical) form.

$x^2 - 6x + 11 = 0$

Hint:

Use the example below.

Example: Solve $x^2+5x+4=0$ by completing the square.

Solution: This method works most efficiently when the coefficient of $x^2$ is $1$ .
Rewrite the equation as $x^2+5x=-4$ . Rewrite the left side as an incomplete square:

$2.5$ $+$ $x$	$2.5x$		$=-4$
$2.5$ $+$ $x$	$x^2$	$2.5x$
	$x+2.5$

Complete the square and rewrite as
$(x+2.5)^2-6.25=-4$ or $(x+2.5)^2=2.25$

Take the square root of both sides, $x+2.5=\underline{+}1.5$ . Solving for $x$ reveals that
$x=-1$ or $x=-4$ .