x2+14x+48=0
complete the square: add 1 to each side
x2+14x+49=1
(x+7)2=1
so (x+7)= 1 or (x+7)=-1
x+7=1 means x=1-7=-6
x+7=-1 means x=-1-7=-8
and x=-8 or x=-6
Check the answer:
(-6)2 -14(6)+48=
36-84+48=0
and 64-112+48=0
You can also solve it with the quadratic formula and a few other ways!
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x2 + 14x + 48 = (x + 8)(x + 6)
49-apex
x2 - 14x + 45 = (x - 9)(x - 5)
x2 - 14x = -49 ∴ x2 - 14x + 49 = 0 ∴ (x - 7)2 = 0 ∴ x = 7
x2+14x+40 = (x+4)(x+10) when factored