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absolute(x^2-9x+7)=7 equation

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Numerical solution:

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The solution

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| 2          |    
|x  - 9*x + 7| = 7
∣(x2−9x)+7∣=7\left|{\left(x^{2} - 9 x\right) + 7}\right| = 7
Simplify
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.

1.
x2−9x+7≥0x^{2} - 9 x + 7 \geq 0
or
(x≤92−532∧−∞<x)∨(532+92≤x∧x<∞)\left(x \leq \frac{9}{2} - \frac{\sqrt{53}}{2} \wedge -\infty < x\right) \vee \left(\frac{\sqrt{53}}{2} + \frac{9}{2} \leq x \wedge x < \infty\right)
we get the equation
(x2−9x+7)−7=0\left(x^{2} - 9 x + 7\right) - 7 = 0
after simplifying we get
x2−9x=0x^{2} - 9 x = 0
the solution in this interval:
x1=0x_{1} = 0
x2=9x_{2} = 9

2.
x2−9x+7<0x^{2} - 9 x + 7 < 0
or
x<532+92∧92−532<xx < \frac{\sqrt{53}}{2} + \frac{9}{2} \wedge \frac{9}{2} - \frac{\sqrt{53}}{2} < x
we get the equation
(−x2+9x−7)−7=0\left(- x^{2} + 9 x - 7\right) - 7 = 0
after simplifying we get
−x2+9x−14=0- x^{2} + 9 x - 14 = 0
the solution in this interval:
x3=2x_{3} = 2
x4=7x_{4} = 7


The final answer:
x1=0x_{1} = 0
x2=9x_{2} = 9
x3=2x_{3} = 2
x4=7x_{4} = 7
The graph
05-15-10-5101520250400
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 0
x1=0x_{1} = 0 
x2 = 2
x2=2x_{2} = 2 
x3 = 7
x3=7x_{3} = 7 
x4 = 9
x4=9x_{4} = 9 
x4 = 9
Sum and product of roots [src] 
sum
2 + 7 + 9
(2+7)+9\left(2 + 7\right) + 9 
=
18
1818 
product
0*2*7*9
9⋅7⋅0⋅29 \cdot 7 \cdot 0 \cdot 2 
=
0
00 
0
Numerical answer [src] 
x1 = 7.0
x2 = 0.0
x3 = 9.0
x4 = 2.0
x4 = 2.0
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