How do you solve an equation by completing the square?

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Firstly, you can only complete the square on quadratic functions (functions in the form Ax2+Bx+C)

If A=1,

Consider B, the coefficient of x. Substitute it into ( x + (B/2) )2

We know if we multiply this out, we will get x2+Bx+(B/2)2

However, we want x2+Bx+C. 

We therefore subtract the (B/2)2 we don't want and add the C we do. 

This gives us ( x + (B/2) )2 - (B/2)2 + C. 

This method is called 'completing the sqaure'

If A does not = 1, manipulate the quadratic so it is in the form A( x+ (B/A) x + (C/A))Solve the bracket as normal and multiply through by A at the end.

 

 

Emma J. GCSE Maths tutor, A Level Maths tutor, GCSE Further Mathemati...

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