Start with 180. <span>Is 180 divisible by 2? Yes, so write "2" as one of the prime factors, and then work with the quotient, 90. </span>
<span>Is 90 divisible by 2? Yes, so write "2" (again) as another prime factor, then work with the quotient, 45. </span>
<span>Is 45 divisible by 2? No, so try a bigger divisor. </span> <span>Is 45 divisible by 3? Yes, so write "3" as a prime factor, then work with the quotient, 15 </span>
<span>Is 15 divisible by 3? [Note: no need to revert to "2", because we've already divided out all the 2's] Yes, so write "3" (again) as a prime factor, then work with the quotient, 5. </span>
<span>Is 5 divisible by 3? No, so try a bigger divisor. </span> Is 5 divisible by 4? No, so try a bigger divisor (actually, we know it can't be divisible by 4 becase it's not divisible by 2) <span>Is 5 divisible by 5? Yes, so write "5" as a prime factor, then work with the quotient, 1 </span>
<span>Once you end up with a quotient of "1" you're done. </span>
<span>In this case, you should have written down, "2 * 2 * 3 * 3 * 5"</span>
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
