find the length of side X in simplest radical form with a rational denominator (giving brainliest and thanks to all!)

x= √10/2

Step-by-step explanation:

if you use trig. functions:

sin 45° = opposite side /hypothenuse = x/√5

sin 45° = √2/ 2

√2/2 = x/√5 multiply both sides by √5

x= (√2*√5)/2 = √10/2

if you use that is a 45-45-90 special triangle

the sides are x, and hypothenuse must be x√2 in this type of triangles so in our case:

x√2 = √5 divide both sides by √2

x= √5/√2 multiply by √2/√2 which =1 and help us get rid of the radical from the denominator

x= (√5*√2)/ (√2*√2) = √10/2

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a