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|x^2+7x|=4x+10 equation

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Numerical solution:

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The solution

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| 2      |           
|x  + 7*x| = 4*x + 10
∣x2+7x∣=4x+10\left|{x^{2} + 7 x}\right| = 4 x + 10
Simplify
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.

1.
x2+7x≥0x^{2} + 7 x \geq 0
or
(0≤x∧x<∞)∨(x≤−7∧−∞<x)\left(0 \leq x \wedge x < \infty\right) \vee \left(x \leq -7 \wedge -\infty < x\right)
we get the equation
−4x+(x2+7x)−10=0- 4 x + \left(x^{2} + 7 x\right) - 10 = 0
after simplifying we get
x2+3x−10=0x^{2} + 3 x - 10 = 0
the solution in this interval:
x1=−5x_{1} = -5
but x1 not in the inequality interval
x2=2x_{2} = 2

2.
x2+7x<0x^{2} + 7 x < 0
or
−7<x∧x<0-7 < x \wedge x < 0
we get the equation
−4x+(−x2−7x)−10=0- 4 x + \left(- x^{2} - 7 x\right) - 10 = 0
after simplifying we get
−x2−11x−10=0- x^{2} - 11 x - 10 = 0
the solution in this interval:
x3=−10x_{3} = -10
but x3 not in the inequality interval
x4=−1x_{4} = -1


The final answer:
x1=2x_{1} = 2
x2=−1x_{2} = -1
The graph
02468-10-8-6-4-21210-250250
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-1 + 2
−1+2-1 + 2 
=
1
11 
product
-2
−2- 2 
=
-2
−2-2 
-2
Rapid solution [src] 
x1 = -1
x1=−1x_{1} = -1 
x2 = 2
x2=2x_{2} = 2 
x2 = 2
Numerical answer [src] 
x1 = 2.0
x2 = -1.0
x2 = -1.0
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