Question

Three algebra questions I don't understand;

Answer 1

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)