Answer and step-by-step explanation:
To find the number, translate the given statement to an algebraic expression first.
Let n be the number.
[tex](n + 2) {}^{2} = n + 4[/tex]
Then simplify the left side of the equation by using the FOIL method.
(n+2)(n+2)
F: n × n = n^2
O: n × 2 = 2n
I: 2 × n = 2n
L: 2 × 2 = 4
= n^2 + 2n + 2n + 4
= n^2 + 4n + 4
Then move n and 4 to the left side of the equation by subtracting them to both sides of the equation.
n^2 + 4n - n + 4 - 4 = n - n + 4 - 4
n^2 + 3n = 0
Then factor the polynomial by dividing them by their GCF which is n.
n(n + 3) = 0
Then equate the two factors to 0.
n = 0
n + 3 = 0
n + 3 - 3 = -3
n = -3
Then check by substituting the values of n to the equation.
(0 + 2)^2 = 0 + 4
4 = 4
(-3 + 2)^2 = -3 + 4
1 = 1
Both equations are true.
The numbers are 0 and -3.
