Mister Exam

Other calculators

x^2-3x-28=0

x^2-3x-28=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               
x  - 3*x - 28 = 0
(x2−3x)−28=0\left(x^{2} - 3 x\right) - 28 = 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=−3b = -3
c=−28c = -28
, then
D = b^2 - 4 * a * c = 

(-3)^2 - 4 * (1) * (-28) = 121

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=−4x_{2} = -4
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−3p = -3
q=caq = \frac{c}{a}
q=−28q = -28
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=3x_{1} + x_{2} = 3
x1x2=−28x_{1} x_{2} = -28
The graph
-2.50.02.55.07.510.012.515.017.520.022.525.0-250250
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-4 + 7
−4+7-4 + 7 
=
3
33 
product
-4*7
−28- 28 
=
-28
−28-28 
-28
Rapid solution [src] 
x1 = -4
x1=−4x_{1} = -4 
x2 = 7
x2=7x_{2} = 7 
x2 = 7
Numerical answer [src] 
x1 = 7.0
x2 = -4.0
x2 = -4.0
The graph
x^2-3x-28=0 equation
    © Mister Exam – Calculator