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Solve $x^{2}+6 x+2=0$ by completing the square
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We cannot use any of the techniques in factorization to solve for $x$. In this situation, we use the technique called completing the square. This makes the quadratic equation into a perfect square trinomial, i.e. the form $a^{2}+2 a b+b^{2}=(a+b)^{2}$.

NOTE: This technique is valid only when 1 is the coefficient of $\mathrm{x}^{2}$.

Here are the steps used to complete the square

Step 1 . Move the constant term to the right:
$$x^{2}+6 x=-2$$

Step 2. Add the square of half the coefficient of $x$ to both sides. In this case, add the square of half of 6 i.e. add the square of 3 .
$$x^{2}+6 x+9=-2+9$$
The left-hand side is now the perfect square of $(x+3) . \quad$ half of the
$$(x+3)^{2}=7$$

We know that if $a^{2}=b, a=\pm b$

Therefore, $x+3=\pm \sqrt{7}$
$$x=-3 \pm \sqrt{7}$$

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