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x^2-5x=0

x^2-5x=0 equation

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Numerical solution:

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The solution

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x  - 5*x = 0
x2−5x=0x^{2} - 5 x = 0
Simplify
Detail solution
This equation is of the form
a∗x2+b∗x+c=0a*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=b2−4acD = b^2 - 4 a c is the discriminant.
Because
a=1a = 1
b=−5b = -5
c=0c = 0
, then
D=b2−4∗a∗c=D = b^2 - 4 * a * c =
(−1)1⋅4⋅0+(−5)2=25\left(-1\right) 1 \cdot 4 \cdot 0 + \left(-5\right)^{2} = 25
Because D > 0, then the equation has two roots.
x1=(−b+D)2ax_1 = \frac{(-b + \sqrt{D})}{2 a}
x2=(−b−D)2ax_2 = \frac{(-b - \sqrt{D})}{2 a}
or
x1=5x_{1} = 5
Simplify
x2=0x_{2} = 0
Simplify
Vieta's Theorem
it is reduced quadratic equation
px+x2+q=0p x + x^{2} + q = 0
where
p=bap = \frac{b}{a}
p=−5p = -5
q=caq = \frac{c}{a}
q=0q = 0
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=5x_{1} + x_{2} = 5
x1x2=0x_{1} x_{2} = 0
The graph
05-15-10-5101520-100100
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x_1 = 0
x1=0x_{1} = 0
Simplify 
x_2 = 5
x2=5x_{2} = 5
Simplify
Sum and product of roots [src] 
sum
0 + 5
(0)+(5)\left(0\right) + \left(5\right) 
=
5
55
Simplify 
product
0 * 5
(0)∗(5)\left(0\right) * \left(5\right) 
=
0
00
Simplify
Numerical answer [src] 
x1 = 5.0
x2 = 0.0
x2 = 0.0
The graph
x^2-5x=0 equation
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