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x^2-5x-14=0

x^2-5x-14=0 equation

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Numerical solution:

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The solution

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x  - 5*x - 14 = 0
(x2−5x)−14=0\left(x^{2} - 5 x\right) - 14 = 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=−5b = -5
c=−14c = -14
, then
D = b^2 - 4 * a * c = 

(-5)^2 - 4 * (1) * (-14) = 81

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

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

or
x1=7x_{1} = 7
x2=−2x_{2} = -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=−5p = -5
q=caq = \frac{c}{a}
q=−14q = -14
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=5x_{1} + x_{2} = 5
x1x2=−14x_{1} x_{2} = -14
The graph
05-15-10-510152025-250250
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-2 + 7
−2+7-2 + 7 
=
5
55 
product
-2*7
−14- 14 
=
-14
−14-14 
-14
Rapid solution [src] 
x1 = -2
x1=−2x_{1} = -2 
x2 = 7
x2=7x_{2} = 7 
x2 = 7
Numerical answer [src] 
x1 = -2.0
x2 = 7.0
x2 = 7.0
The graph
x^2-5x-14=0 equation
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