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x^2+x-4=0

x^2+x-4=0 equation

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Numerical solution:

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The solution

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 2            
x  + x - 4 = 0
(x2+x)−4=0\left(x^{2} + x\right) - 4 = 0
Simplify
Detail solution
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=1b = 1
c=−4c = -4
, then
D = b^2 - 4 * a * c = 

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

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

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

or
x1=−12+172x_{1} = - \frac{1}{2} + \frac{\sqrt{17}}{2}
x2=−172−12x_{2} = - \frac{\sqrt{17}}{2} - \frac{1}{2}
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=1p = 1
q=caq = \frac{c}{a}
q=−4q = -4
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−1x_{1} + x_{2} = -1
x1x2=−4x_{1} x_{2} = -4
The graph
05-15-10-51015-200200
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
             ____
       1   \/ 17 
x1 = - - + ------
       2     2
x1=−12+172x_{1} = - \frac{1}{2} + \frac{\sqrt{17}}{2} 
             ____
       1   \/ 17 
x2 = - - - ------
       2     2
x2=−172−12x_{2} = - \frac{\sqrt{17}}{2} - \frac{1}{2} 
x2 = -sqrt(17)/2 - 1/2
Sum and product of roots [src] 
sum
        ____           ____
  1   \/ 17      1   \/ 17 
- - + ------ + - - - ------
  2     2        2     2
(−172−12)+(−12+172)\left(- \frac{\sqrt{17}}{2} - \frac{1}{2}\right) + \left(- \frac{1}{2} + \frac{\sqrt{17}}{2}\right) 
=
-1
−1-1 
product
/        ____\ /        ____\
|  1   \/ 17 | |  1   \/ 17 |
|- - + ------|*|- - - ------|
\  2     2   / \  2     2   /
(−12+172)(−172−12)\left(- \frac{1}{2} + \frac{\sqrt{17}}{2}\right) \left(- \frac{\sqrt{17}}{2} - \frac{1}{2}\right) 
=
-4
−4-4 
-4
Numerical answer [src] 
x1 = 1.56155281280883
x2 = -2.56155281280883
x2 = -2.56155281280883
The graph
x^2+x-4=0 equation
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