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sqrt(-72-17x)=-x

sqrt(-72-17x)=-x equation

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Numerical solution:

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The solution

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\/ -72 - 17*x  = -x
−17x−72=−x\sqrt{- 17 x - 72} = - x
Simplify
Detail solution
Given the equation
−17x−72=−x\sqrt{- 17 x - 72} = - x
−17x−72=−x\sqrt{- 17 x - 72} = - x
We raise the equation sides to 2-th degree
−17x−72=x2- 17 x - 72 = x^{2}
−17x−72=x2- 17 x - 72 = x^{2}
Transfer the right side of the equation left part with negative sign
−x2−17x−72=0- x^{2} - 17 x - 72 = 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=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=−1a = -1
b=−17b = -17
c=−72c = -72
, then
D = b^2 - 4 * a * c = 

(-17)^2 - 4 * (-1) * (-72) = 1

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

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

or
x1=−9x_{1} = -9
x2=−8x_{2} = -8

Because
−17x−72=−x\sqrt{- 17 x - 72} = - x
and
−17x−72≥0\sqrt{- 17 x - 72} \geq 0
then
−x≥0- x \geq 0
or
x≤0x \leq 0
−∞<x-\infty < x
The final answer:
x1=−9x_{1} = -9
x2=−8x_{2} = -8
The graph
20-18-16-14-12-10-8-6-4-2-2525
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -9
x1=−9x_{1} = -9 
x2 = -8
x2=−8x_{2} = -8 
x2 = -8
Sum and product of roots [src] 
sum
-9 - 8
−9−8-9 - 8 
=
-17
−17-17 
product
-9*(-8)
−−72- -72 
=
72
7272 
72
Numerical answer [src] 
x1 = -9.0
x2 = -8.0
x2 = -8.0
The graph
sqrt(-72-17x)=-x equation
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