A perfect square quadratic has the form (a+b)^2=a^2+2ab+b^2 We need to substitute what is given and try to find a and b
22. x^2+10x+c so we see that a=x this means that 2ab=10x, substitute a=x and factor out both sides or 2x(b)=2x(5) so b=5 and c=b^2=5^2=25
23. x^2+13x+c Similarly, we see that a=x substitute x=a in the second term, 13x=2a(b)=2x(b) again, factor out 2x on both sides 2x(6.5)=2x(b) allows us to see that b=6.5, or b=13/2 c=b^2=(13/2)^2=13^2/2^2=169/4
23. x^2+10x=18 Now we complete the square by adding c=b^2 on both sides x^2+2(5x)+5^2=18+5^2 (x+5)^2 = 18+25 Take square root, x+5= ± 43 x=-5 ± 6.557 (to three decimals) x={-11.56, 1.56} (to two decimals)
The answer is 36. Say 42 + 42 is 84. Since one of the number is 6 more than the other, add 6 the first 42 and subtract 6 from the other number which will be 48 + 36 = 84. So the smaller of the two is 36.
