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Check whether the following is a quadratic equation.((x+1)^{2}=2(x-3))

Question

 Check whether the following is a quadratic equation.
\((x+1)^{2}=2(x-3)\)

Answer

Yes, it is a quadratic equation
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Solution

Given equation is
\((x+1)^{2}=2(x-3)\)
\(\Rightarrow x^{2}+2x+1=2x-6\)         \([\because (a+b)^{2}=a^{2}+2ab+b^{2}]\)
  \(\Rightarrow x^{2}+1+6=0\)
\(\Rightarrow x^{2}+7=0\)
which is of the form \(ax^{2}+bx+c=0\) ,where\(a=1,b=0,c=7\).
Thus, \((x+1)^{2}=2(x-3)\)is a quadratic equation.
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