Question

Find x so the distance between (x, 2) and (2, 4) is the square root of 13. How do you work this?

Answer 1

$d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ \sqrt{13} = \sqrt{(2-x_1)^2+(4-2)^2} \\ \\ \sqrt{13} = \sqrt{(2-x_1)^2+(2)^2} \\ \\ \sqrt{13} = \sqrt{(2-x_1)^2+4} \\ \\ \sqrt{13} = \sqrt{(2-x_1)*(2-x_1)+4} \\ \\ \sqrt{13} = \sqrt{4-2x_1-2x_1+(x_1)^2+4} \\ \\ (\sqrt{13})^2 = (\sqrt{-4x_1+(x_1)^2+8})^2 \\ \\ 13=(x_1)^2-4x_1+8 \\ \\ (x_1)^2-4x_1-5=0 \\ \\ (x_1-5)(x_1+1)=0 \\ \\ x_1=5,x_1=-1$

x can either equal 5 or -1