Answer:
x=11
x=−5
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 6*x+55-(x^2)=0
-x2+6x+55 =0
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 = 6
C = 55
Accordingly, B2 - 4AC =
36 - (-220) =
256
Applying the quadratic formula :
-6 ± √ 256
x = ——————
-2
Can √ 256 be simplified ?
Yes! The prime factorization of 256 is
2•2•2•2•2•2•2•2
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).
√ 256 = √ 2•2•2•2•2•2•2•2 =2•2•2•2•√ 1 =
± 16 • √ 1 =
± 16
So now we are looking at:
x = ( -6 ± 16) / -2
Two real solutions:
x =(-6+√256)/-2=3-8= -5.000
or:
x =(-6-√256)/-2=3+8= 11.000
