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(x-5)(x-1)-21=0

(x-5)(x-1)-21=0 equation

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Numerical solution:

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The solution

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(x - 5)*(x - 1) - 21 = 0
(x5)(x1)21=0\left(x - 5\right) \left(x - 1\right) - 21 = 0
Detail solution
Expand the expression in the equation
(x5)(x1)21=0\left(x - 5\right) \left(x - 1\right) - 21 = 0
We get the quadratic equation
x26x16=0x^{2} - 6 x - 16 = 0
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
x1=Db2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=Db2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=6b = -6
c=16c = -16
, then
D = b^2 - 4 * a * c = 

(-6)^2 - 4 * (1) * (-16) = 100

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
x1=8x_{1} = 8
x2=2x_{2} = -2
The graph
05-15-10-510152025-250250
Rapid solution [src]
x1 = -2
x1=2x_{1} = -2
x2 = 8
x2=8x_{2} = 8
x2 = 8
Sum and product of roots [src]
sum
-2 + 8
2+8-2 + 8
=
6
66
product
-2*8
16- 16
=
-16
16-16
-16
Numerical answer [src]
x1 = 8.0
x2 = -2.0
x2 = -2.0
The graph
(x-5)(x-1)-21=0 equation