Answer:
Step-by-step explanation:
To begin, get everything but the x terms on one side of the equation by subtracting the 62. That gives us
[tex]x^2+16x=-55[/tex]
Next, take half the linear term, square it, and add it to both sides. Our linear term is 16. Half of 16 is 8, and 8 squared is 6, so add 64 to both sides:
[tex]x^2+16x+64=9[/tex]
The reason we do this is to get a perfect square binomial on the left, which looks like this:
[tex](x+8)^2=9[/tex]. Undo the squaring on the left by taking the square root of both sides. Doing this leaves x + 8 on the left, but + or - 3 on the right:
x + 8 = 3 and x + 8 = -3. Solving each of these equations gives you your 2 solutions:
x = -5 and x = -11
