Mister Exam

Other calculators

23x-10+5x^2=0

23x-10+5x^2=0 equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
               2    
23*x - 10 + 5*x  = 0
5x2+(23x−10)=05 x^{2} + \left(23 x - 10\right) = 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=5a = 5
b=23b = 23
c=−10c = -10
, then
D = b^2 - 4 * a * c = 

(23)^2 - 4 * (5) * (-10) = 729

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

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

or
x1=25x_{1} = \frac{2}{5}
x2=−5x_{2} = -5
Vieta's Theorem
rewrite the equation
5x2+(23x−10)=05 x^{2} + \left(23 x - 10\right) = 0
of
ax2+bx+c=0a x^{2} + b x + c = 0
as reduced quadratic equation
x2+bxa+ca=0x^{2} + \frac{b x}{a} + \frac{c}{a} = 0
x2+23x5−2=0x^{2} + \frac{23 x}{5} - 2 = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=235p = \frac{23}{5}
q=caq = \frac{c}{a}
q=−2q = -2
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−235x_{1} + x_{2} = - \frac{23}{5}
x1x2=−2x_{1} x_{2} = -2
The graph
02468-6-4-2101214-10001000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -5
x1=−5x_{1} = -5 
x2 = 2/5
x2=25x_{2} = \frac{2}{5} 
x2 = 2/5
Sum and product of roots [src] 
sum
-5 + 2/5
−5+25-5 + \frac{2}{5} 
=
-23/5
−235- \frac{23}{5} 
product
-5*2
----
 5
−2- 2 
=
-2
−2-2 
-2
Numerical answer [src] 
x1 = 0.4
x2 = -5.0
x2 = -5.0
The graph
23x-10+5x^2=0 equation
    © Mister Exam – Calculator