simplylogic0317 simplylogic0317

22-08-2018
Mathematics

contestada

Solve the equation for all values of x by completing the square.

x^2+8x=9

Respuesta :

30-08-2018

[tex] (*)\qquad(a+b)^2=a^2+2ab+b^2\\\\x^2+8x=9\\\\x^2+2\cdot x\cdot4=9\ \ \ \ |+4^2\\\\\underbrace{x^2+2\cdot x\cdot4+4^2}_{(*)}=9+4^2\\\\(x+4)^2=25\to x+4=\pm\sqrt{25}\\\\x+4=-5\ \vee\ x+4=5\ \ \ \ \ |-4\\\\x=-9\ \vee\ x=1 [/tex]

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