Question

solve the following quadratic equation by completing the square: $x^{2}+18x + 17=0$

Explanation:

Step1: Isolate the x - terms

$x^{2}+18x=-17$

Step2: Find the value to complete the square

The coefficient of $x$ is $18$. Half of it is $\frac{18}{2} = 9$, and its square is $9^{2}=81$. Add 81 to both sides of the equation.
$x^{2}+18x + 81=-17 + 81$

Step3: Rewrite the left - hand side as a perfect square

$(x + 9)^{2}=64$

Step4: Take the square root of both sides

$x+9=\pm\sqrt{64}=\pm8$

Step5: Solve for x

When $x + 9 = 8$, $x=8 - 9=-1$; when $x + 9=-8$, $x=-8 - 9=-17$.

Answer:

$x=-1$ or $x=-17$