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Bolton
Mathematics
6 June, 20:58
5x^2=x+1 solve using completion of squares
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Jane Morales
6 June, 20:59
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Take everything to one side and equate it to zero
So: 5x^2 - x - 1=0
Next factorise so it's 5 (x^2-1/5) - 1=0
So: 5 (x-1/5) ^2 - 1=0
So complete the square
First of all remove the five by division (x - ((1/5) / 2) ^2 + (1/5/2) ^2) - 1 = 0
So (x - 1/10) ^2 + 1/5 + 1/100 = 0
Answer is (x-1/10) ^2 - 21/100 = 0
Take - 21/100 to the other side so:
(x-1/10) ^2 = 21/100
Square root both sides so
(X-1/10) = square root of 21/100
Take - 1/10 to the other side so
X = 1/10 + square root of 21/100
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