Respuesta :

WojtekR

To solve this equation we could use:


[tex] a^2-b^2=(a+b)(a-b) [/tex]


There will be:


[tex] 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}} [/tex]

gmany

[tex]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[/tex]

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