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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

You have entered [src] 
 2               
x  + 5*x - 14 = 0
x2+5x−14=0x^{2} + 5 x - 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=2x_{1} = 2
Simplify
x2=−7x_{2} = -7
Simplify
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
05-25-20-15-10-51015-250250
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -7
x1=−7x_{1} = -7
Simplify 
x2 = 2
x2=2x_{2} = 2
Simplify
Sum and product of roots [src] 
sum
0 - 7 + 2
(−7+0)+2\left(-7 + 0\right) + 2 
=
-5
−5-5 
product
1*-7*2
1(−7)21 \left(-7\right) 2 
=
-14
−14-14 
-14
Numerical answer [src] 
x1 = 2.0
x2 = -7.0
x2 = -7.0
The graph
x^2+5x-14=0 equation
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