# The sum of the square of a positive number and the square of 2 more than the number is 74. What is the number?

Dec 12, 2016

Let the number be $x$.

${x}^{2} + {\left(x + 2\right)}^{2} = 74$

${x}^{2} + {x}^{2} + 4 x + 4 = 74$

$2 {x}^{2} + 4 x - 70 = 0$

$2 \left({x}^{2} + 2 x - 35\right) = 0$

$\left(x + 7\right) \left(x - 5\right) = 0$

$x = - 7 \mathmr{and} 5$

$\therefore$ The number is $5$.

Hopefully this helps!