Mister Exam

Other calculators

16x+9-4x²=9 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    
16*x + 9 - 4*x  = 9
−4x2+(16x+9)=9- 4 x^{2} + \left(16 x + 9\right) = 9
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
−4x2+(16x+9)=9- 4 x^{2} + \left(16 x + 9\right) = 9
to
(−4x2+(16x+9))−9=0\left(- 4 x^{2} + \left(16 x + 9\right)\right) - 9 = 0
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=−4a = -4
b=16b = 16
c=0c = 0
, then
D = b^2 - 4 * a * c = 

(16)^2 - 4 * (-4) * (0) = 256

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

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

or
x1=0x_{1} = 0
x2=4x_{2} = 4
Vieta's Theorem
rewrite the equation
−4x2+(16x+9)=9- 4 x^{2} + \left(16 x + 9\right) = 9
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
x2−4x=0x^{2} - 4 x = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−4p = -4
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=4x_{1} + x_{2} = 4
x1x2=0x_{1} x_{2} = 0
The graph
05-15-10-5101520-1000500
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 0
x1=0x_{1} = 0 
x2 = 4
x2=4x_{2} = 4 
x2 = 4
Sum and product of roots [src] 
sum
4
44 
=
4
44 
product
0*4
0⋅40 \cdot 4 
=
0
00 
0
Numerical answer [src] 
x1 = 4.0
x2 = 0.0
x2 = 0.0
    © Mister Exam – Calculator