Respuesta :
Answer:
(a)
[tex](x+1)^2=32[/tex]
(b)
[tex](x+1-\sqrt{32})(x+1+\sqrt{32}) =0[/tex]
Step-by-step explanation:
We are given
[tex]x^2+2x=31[/tex]
Since, we have to complete square
so, we can use formula
[tex]a^2+2ab+b^2=(a+b)^2[/tex]
[tex]x^2+2\times x\times 1=31[/tex]
so, we can add both sides by 1^2
[tex]x^2+2\times x\times 1+1^2=31+1^2[/tex]
now, we can use formula
and we get
[tex](x+1)^2=32[/tex]
so, equation after completing square is
[tex](x+1)^2=32[/tex]
now, we can solve for x
we can move all terms on left side
[tex](x+1)^2-32=0[/tex]
[tex](x+1)^2-(\sqrt{32})^2 =0[/tex]
now, we can factor it
[tex](x+1-\sqrt{32})(x+1+\sqrt{32}) =0[/tex]
