Answer
4 and 6 or
-6 and - 4
Work Step by Step
This is the working equation for the problem:
$x^{2} + (x+2)^{2}=52$
Solve the equation.
$x^{2} + (x+2)^{2}=52$
expand $(x+2)^{2}$
$x^{2} + x^{2} + 4x + 4 = 52$
add the two $x{2}$s together and subtract $4$ to $52$
$2x^{2} + 4x = 48$
divide the equation by $2$
$x^{2}+2x=24$
use factoring and zero product property to identify the integers
$x^{2}+2x-24=0$
$(x+6)(x-4)=0$
$x+6=0$
$x=-6$
$x-4=0$
$x=4$
Since the square of an integer (whether it has positive or negative value) will always have a positive value, we must take into consideration the signs of the two consecutive even numbers.
So the answers will either be number pairs 4 & 6 or -6 & -4.
