Answer:
[tex]\Huge \boxed{x=-1}[/tex]
Step-by-step explanation:
[tex]x^2+2x=-1[/tex]
Adding 1 to both sides of the equation.
[tex]x^2+2x+1=-1+1[/tex]
[tex]x^2 +2x+1=0[/tex]
Factoring the left side of the equation.
[tex]x^2 +1x+1x+1=0[/tex]
[tex]x(x+1)+1(x+1)=0[/tex]
[tex](x+1)(x+1) = 0[/tex]
[tex](x+1)^2 =0[/tex]
Taking the square root of both sides of the equation.
[tex]\sqrt{(x+1)^2} =\sqrt{0}[/tex]
[tex]x+1=0[/tex]
Subtracting 1 from both sides of the equation.
[tex]x+1-1=0-1[/tex]
[tex]x=-1[/tex]
Answer:
x = -1
Step-by-step explanation:
[tex]x^2+2x = -1\\=0\\=x^2+2x+1 \\= (x+1)(x+1)\\=(x+1)^2\\\\0 = \sqrt{(x+1)^2} \\= x+1\\\\x+1=0\\x=-1[/tex]
