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Please solve: x^2+10x+25=9

Sagot :

[tex]x^2+10x+25=9\\\\\underbrace{x^2+2x\cdot5+5^2}_{(*)}=9\\\\(x+5)^2=9\iff x+5=3\ or\ x+5=-3\\\\x=3-5\ or\ x=-5-3\\\\\boxed{x=-2\ or\ x=-8}\leftarrow solutions[/tex]

[tex](*)\ (a+b)^2=a^2+2ab+b^2[/tex]


[tex]other\ methode:\\\\x^2+10x+25=9\\\\x^2+10x+25-9=0\\\\x^2+10x+16=0\\\\x^2+2x+8x+16=0\\\\x(x+2)+8(x+2)=0\\\\(x+2)(x+8)=0\iff x+2=0\ or\ x+8=0\\\\\boxed{x=-2\ or\ x=-8}[/tex]
konrad509
[tex]x^2+10x+25=9\\ (x+5)^2=9\\ x+5=3 \vee x+5=-3\\ x=-2 \vee x=-8[/tex]
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