Find the roots of the equation y=x^2-8x+5 by completing the square.
Firstly, we need to look at completing the square. This is done by looking at the x^2-8x section of the equation. We need to find a way of converting it to the format of (x-a)^2. If you remember, when multiplying out brackets, the first x will be squared and the second x term will be ax2. Therefore, we find that (x-4)^2 will produce x^2-8x+16. This 16 didn't exist before so we must subtract this from our equation. We therefore produce: y=(x-4)^2+5-16 = (x-4)^2-11
We must then make y=0 as we are trying to find the roots - where the graph crosses the x axis.
a) 0=(x-4)^2-11 - add 11 to both sides. b) 11=(x-4)^2 - square root both sides not forgetting the plus or minus. c) +/-11^1/2 = x-4 - add 4 to both sides. d) x=4+11^1/2 or 4-11^1/2
You have now found the 2 roots of the equation.
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