Question

solve x(x-1)=1 by completing the square method

Answer 1

Step-by-step explanation:

x^2-x-1=0

(x-1/2)^2-5/4=0

(x-1/2)^2=5/4

x-1/2=sqrt(5)/2

x=(sqrt(5)+1)/2

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Answer 2

Answer:

Given:

$\tt x(x-1)=x$  to be solved by completing the square method.

Solution:

$\:\:\:\:\:\:\:\:\:\tt x(x-1)=x\\ \implies{x^{2} -1=x}\\\implies x^{2} -x = 1$

• Divide the equation by the coefficient of $\tt x^{2}$.  

$\tt x^{2} -\dfrac{1}{1} x=\dfrac{1}{1}$

• Add the square of half the coefficient to $\tt x$.

$\:\:\:\:\:\:\:\:\: \tt x^{2} -x+{(\dfrac{1}{2}})^ {2} =1+ ( {\dfrac{1}{2} })^{2}\\\\\\ \implies {(x^{2}-\dfrac{1}{2} } ) ^{2} =1+\dfrac{1}{4} =\dfrac{5}{4} \\\\\\ \implies x-\dfrac{1}{2} =\pm \sqrt{\dfrac{1}{4} } =\pm\dfrac{\sqrt{5} }{2} \\\\\\ \implies \boxed{\tt{x=\dfrac{1}{2} \pm \dfrac{1}{2}}}$

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