Question

the movement of the progress bar may be uneven because questions can be worth more or less
solve: $x^2 + 20x = -20$
$\circ$ $x = -10 \pm 4\sqrt{5}$
$\circ$ $x = 4\sqrt{5} \pm 10$
$\circ$ $x = -10 + \sqrt{80}$
$\circ$ $x = 10 \pm \sqrt{80}$

Explanation:

Step1: Convert to standard quadratic form

We start with the equation \(x^{2}+20x=-20\). To complete the square, we first rewrite it in the standard form \(x^{2}+20x + 20=0\). But for completing the square, we take the equation \(x^{2}+20x=-20\). The coefficient of \(x\) is \(20\), half of it is \(10\), and squaring it gives \(100\). We add \(100\) to both sides:
\(x^{2}+20x + 100=-20 + 100\)

Step2: Simplify both sides

The left - hand side is a perfect square: \((x + 10)^{2}\), and the right - hand side is \(80\). So we have \((x + 10)^{2}=80\)

Step3: Take square roots

Taking the square root of both sides, we get \(x+10=\pm\sqrt{80}\). Since \(\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}\)

Step4: Solve for x

Subtract \(10\) from both sides: \(x=-10\pm4\sqrt{5}\)

Answer:

\(x = - 10\pm4\sqrt{5}\) (corresponding to the first option: \(x=-10\pm4\sqrt{5}\))