Description
(k+1)(k-5)=0

Explanation & Answer

k+1)(k-5)=0
=>k+1=0;or k-5=0
=>k=-1;k=5.
hence
Solve Quadratic Equation by Completing The Square
4.2 Solving k2-4k-5 = 0 by Completing The Square .
Add 5 to both side of the equation :
k2-4k = 5
Now the clever bit: Take the coefficient of k , which is 4 , divide by two, giving 2 , and finally square it giving 4
Add 4 to both sides of the equation :
On the right hand side we have :
5 + 4 or, (5/1)+(4/1)
The common denominator of the two fractions is 1 Adding (5/1)+(4/1) gives 9/1
So adding to both sides we finally get :
k2-4k+4 = 9
Adding 4 has completed the left hand side into a perfect square :
k2-4k+4 =
(k-2) • (k-2) =
(k-2)2
Things which are equal to the same thing are also equal to one another. Since
k2-4k+4 = 9 and
k2-4k+4 = (k-2)2
then, according to the law of transitivity,
(k-2)2 = 9
We'll refer to this Equation as Eq. #4.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(k-2)2 is
(k-2)2/2 =
(k-2)1 =
k-2
Now, applying the Square Root Principle to Eq. #4.2.1 we get:
k-2 = √ 9
Add 2 to both sides to obtain:
k = 2 + √ 9
Since a square root has two values, one positive and the other negative
k2 - 4k - 5 = 0
has two solutions:
k = 2 + √ 9
or
k = 2 - √ 9
Solve Quadratic Equation using the Quadratic Formula
4.3 Solving k2-4k-5 = 0 by the Quadratic Formula .
According to the Quadratic Formula, k , the solution for Ak2+Bk+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
k = ————————
2A In our case, A = 1
B = -4
C = -5 Accordingly, B2 - 4AC =
16 - (-20) =
36Applying the quadratic formula :
4 ± √ 36
k = —————
2Can √ 36 be simplified ?
Yes! The prime factorization of 36 is
2•2•3•3
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 36 = √ 2•2•3•3 =2•3•√ 1 =
± 6 • √ 1 =
± 6
So now we are looking at:
k = ( 4 ± 6) / 2
Two real solutions:
k =(4+√36)/2=2+3= 5.000
or:
k =(4-√36)/2=2-3= -1.000
Two solutions were found :
- k = 5
- k = -1
