How do you solve an equation by completing the square?
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( x2 + (B/A) x + (C/A)). Solve the bracket as normal and multiply through by A at the end.
EJ
Related Maths A Level answers
All answers ▸Given f(x) = (x^4 - 1) / (x^4 + 1), use the quotient rule to show that f'(x) = nx^3 / (x^4 + 1)^2 where n is an integer to be determined.
ln(2x^2 + 9x – 5) = 1 + ln(x^2 + 2x – 15). Express x in terms of e
A circle with centre C has equation x^2 + y^2 + 2x + 6y - 40 = 0 . Express this equation in the form (x - a)^2 + (x - b)^2 = r^2. Find the co-ordinates of C and the radius of the circle.
f(x) = x^3 + 3x^2 + 5. Find (a) f ′′(x), (b) ∫f(x)dx.