Question

Solve the following quadratic equation. 3(x + 5)^2 = 60

Answer 1

$3(x+5)^2=60\ \ \ |:3\\\\(x+5)^2=20\iff x+5=\pm\sqrt{20}\ \ \ |-5\\\\x=-5\pm\sqrt{20}\\\\20=4\cdot5\to\sqrt{20}=\sqrt4\cdot\sqrt5=2\sqrt5\\\\Answer:\ x=-5-2\sqrt5\ \vee\ x=-5+2\sqrt5$

Answer 2

To solve this equation we could use:

$a^2-b^2=(a+b)(a-b)$

There will be:

$3(x + 5)^2 = 60\qquad|:3\\\\(x+5)^2=20\\\\(x+5)^2=\big(\sqrt{20}\big)^2\\\\ (x+5)^2=\big(\sqrt{4\cdot5}\big)^2\\\\(x+5)^2=\big(\sqrt{4}\cdot\sqrt{5}\big)^2\\\\(x+5)^2=\big(2\sqrt{5}\big)^2\\\\(x+5)^2-\big(2\sqrt{5}\big)^2=0\\\\ (x+5+2\sqrt{5})(x+5-2\sqrt{5})=0\\\\\\x+5+2\sqrt{5}=0\qquad\vee\qquad x+5-2\sqrt{5}=0\\\\\boxed{x=-5-2\sqrt{5}\qquad\vee\qquad x=-5+2\sqrt{5}}$