Question

solve by completing the square and applying the square root property. express the solution set in exact simplest form.\\(x^{2}+20x - 4 = 0\\)

Explanation:

Step1: Isolate constant term

$x^2 + 20x = 4$

Step2: Complete the square

$x^2 + 20x + 100 = 4 + 100$
$(x + 10)^2 = 104$

Step3: Apply square root property

$x + 10 = \pm\sqrt{104}$

Step4: Simplify radical and solve for x

$\sqrt{104} = \sqrt{4 \times 26} = 2\sqrt{26}$
$x = -10 \pm 2\sqrt{26}$

Answer:

$x = -10 + 2\sqrt{26}$ and $x = -10 - 2\sqrt{26}$