Answer:
[tex] [/tex]
x = 0 and –3
Step-by-step explanation:
let x = be the number
[tex](x + 2) {}^{2} = x + 4[/tex]
[tex]x {}^{2} + 4x + 4 = x + 4[/tex]
[tex]x {}^{2} + 4x + 4 - x - 4 = 0[/tex]
combine similar terms
[tex]x {}^{2} + 3x = 0[/tex]
[tex]x(x + 3) = 0[/tex]
[tex]x = 0[/tex]
[tex]x + 3 = 0[/tex]
[tex]x = 0 - 3[/tex]
[tex]x = - 3[/tex]
Therefore x = 0 and –3
CHECKING:
x = 0
[tex](x + 2) {}^{2} = x + 4[/tex]
[tex](0 + 2) {}^{2} = 0 + 4[/tex]
[tex]2 {}^{2} = 4[/tex]
[tex]4 = 4[/tex]
x = –3
[tex](x + 2) {}^{2} = x + 4[/tex]
[tex]( - 3 + 2) {}^{2} = - 3 + 4[/tex]
[tex]( - 1) {}^{2} = 1[/tex]
[tex]1 = 1[/tex]
