find t :
√(t^2-10t+50)
Answers
Answer:
75
Step-by-step explanation:
2.2 Solving t2-10t-50 = 0 by Completing The Square .
Add 50 to both side of the equation :
t2-10t = 50
Now the clever bit: Take the coefficient of t , which is 10 , divide by two, giving 5 , and finally square it giving 25
Add 25 to both sides of the equation :
On the right hand side we have :
50 + 25 or, (50/1)+(25/1)
The common denominator of the two fractions is 1 Adding (50/1)+(25/1) gives 75/1
So adding to both sides we finally get :
t2-10t+25 = 75
Adding 25 has completed the left hand side into a perfect square :
t2-10t+25 =
(t-5) • (t-5) =
(t-5)2
Things which are equal to the same thing are also equal to one another. Since
t2-10t+25 = 75 and
t2-10t+25 = (t-5)2
then, according to the law of transitivity,
(t-5)2 = 75
We'll refer to this Equation as Eq. #2.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(t-5)2 is
(t-5)2/2 =
(t-5)1 =
t-5
Now, applying the Square Root Principle to Eq. #2.2.1 we get:
t-5 = √ 75
Add 5 to both sides to obtain:
t = 5 + √ 75
Since a square root has two values, one positive and the other negative
t2 - 10t - 50 = 0
has two solutions:
t = 5 + √ 75
or
t = 5 - √ 75