Use Pythagorean's Theorem to solve for c. [tex]c^2=(2 \sqrt{x^2+3x})^2+(3)^2 [/tex]. We will simplify the right side by squaring both terms. [tex]c^2=4(x^2+3x)+9[/tex] which simplifies even further to [tex]c^2=4x^2+12x+9[/tex]. In that polynomial, the leading coefficient, 4, is a perfect square, and so is the constant at the end, 9. So that polynomial is the sum of perfect squares. It will break down like this: [tex]c^2=(2x+3)^2[/tex] so then taking the square root of both sides gives us that c = 2x + 3, choice on the top right.
