Solving -x2+12x+12 = 0 by the Quadratic Formula .
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 = -1
B = 12
C = 12
Accordingly, B2 - 4AC =
144 - (-48) =
192
Applying the quadratic formula :
-12 ± √ 192
x = ——————
-2
Can √ 192 be simplified ?
Yes! The prime factorization of 192 is
2•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).
√ 192 = √ 2•2•2•2•2•2•3 =2•2•2•√ 3 =
± 8 • √ 3
√ 3 , rounded to 4 decimal digits, is 1.7321
So now we are looking at:
x = ( -12 ± 8 • 1.732 ) / -2
Two real solutions:
x =(-12+√192)/-2=6-4√ 3 = -0.928
or:
x =(-12-√192)/-2=6+4√ 3 = 12.928
x =(-12-√192)/-2=6+4√ 3 = 12.928
x =(-12+√192)/-2=6-4√ 3 = -0.928
These are the two solutions
Hope my answer helps!