Question

x + raiz de 2x + 5 = 15 conta resolvida

Answer 1

$Resolu\c{c}\~ao \to \left\{\begin{array}{ccc}x+\sqrt{2x+5} = 15\\\\\sqrt{2x+5} = 15-x\\\\(\sqrt{2x+5})^2 = (15-x)^2\\\\2x+5 =(15)^2-2*(15)(x)+(x)^2\\\\2x+5 = 225 -30x+x^2\\\\x^2-30x+225-2x-5=0\\\\x^2-32x+220 = 0\\\\x = \frac{-(-32)\pm\sqrt{(-32)^2-4*(1)*(220)}}{2*(1)} \\\\x = \frac{32\pm\sqrt{1024-880}}{2}\\\\x = \frac{32\pm\sqrt{144}}{2}\\\\x = \frac{32\pm12}{2} \to \left\{\begin{array}{ccc}x' = \frac{32+12}{2} = 22\\\\x'' = \frac{32-12}{2} = 10 \end{array}\right\\\\\boxed{S = \{10\}}\end{array}\right$

O 22 não é solução porque não é raiz da equação.

Espero ter ajudado =^.^=