Answer:
x = 8
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
= 
Note that ΔBCD is a 3- 4- 5 triangle ( Pythagorean triple), hence CD = 4
Substitute given values into the equation
= 
( cross- multiply )
3x = 24 ( divide both sides by 3 )
x = 8
None? Unless the second option is supposed to be 10^2 or the fourth option is 50 x 2.
Perentheses, probably do multiplication.
"Completing the square" is the process used to derive the quadratic formula for the general quadratic ax^2+bx+c=0. Suppose you did not know the value of a,b, or c of the quadratic...
ax^2+bx+c=0 You need a leading coefficient of one for the process to work, so you divide the whole equation by a
x^2+bx/a+c/a=0 now you move the constant to the other side of the equation
x^2+bx/a=-c/a now you halve the linear coefficient, square that, then add that value to both sides, ie, (b/(2a))^2=b^2/(4a^2)...
x^2+bx/a+b^2/(4a^2)=b^2/(4a^2)-c/a now the left side is a perfect square...
(x+b/(2a))^2=(b^2-4ac)/(4a^2) now take the square root of both sides
x+b/(2a)=±√(b^2-4ac)/(2a) now subtract b/(2a) from both sides
x=(-b±√(b^2-4ac))/(2a)
It is actually much simpler keeping track of everything when using known values for a,b, and c, but the above explains the actual process used to create the quadratic formula, which the above solution is. :)
