Solve 4x²-4x+5=0 by completing squares method.
Answers
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 4
B = -4
C = -5
Accordingly, B2 - 4AC =
16 - (-80) =
96
Applying the quadratic formula :
4 ± √ 96
x = —————
8
Can √ 96 be simplified ?
Yes! The prime factorization of 96 is
2•2•2•2•2•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).
√ 96 = √ 2•2•2•2•2•3 =2•2•√ 6 =
± 4 • √ 6
√ 6 , rounded to 4 decimal digits, is 2.4495
So now we are looking at:
x = ( 4 ± 4 • 2.449 ) / 8
Two real solutions:
x =(4+√96)/8=(1+√ 6 )/2= 1.725
or:
x =(4-√96)/8=(1-√ 6 )/2= -0.725
Two solutions were found :
x =(4-√96)/8=(1-√ 6 )/2= -0.725
x =(4+√96)/8=(1+√ 6 )/2= 1.725