Mister Exam

Other calculators

4b^2=144 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      
4*b  = 144
4b2=1444 b^{2} = 144
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
4b2=1444 b^{2} = 144
to
4b2−144=04 b^{2} - 144 = 0
This equation is of the form
a*b^2 + b*b + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
b1=D−b2ab_{1} = \frac{\sqrt{D} - b}{2 a}
b2=−D−b2ab_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=4a = 4
b=0b = 0
c=−144c = -144
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (4) * (-144) = 2304

Because D > 0, then the equation has two roots.
b1 = (-b + sqrt(D)) / (2*a)

b2 = (-b - sqrt(D)) / (2*a)

or
b1=6b_{1} = 6
b2=−6b_{2} = -6
Vieta's Theorem
rewrite the equation
4b2=1444 b^{2} = 144
of
ab2+b2+c=0a b^{2} + b^{2} + c = 0
as reduced quadratic equation
b2+b2a+ca=0b^{2} + \frac{b^{2}}{a} + \frac{c}{a} = 0
b2−36=0b^{2} - 36 = 0
b2+bp+q=0b^{2} + b p + q = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=−36q = -36
Vieta Formulas
b1+b2=−pb_{1} + b_{2} = - p
b1b2=qb_{1} b_{2} = q
b1+b2=0b_{1} + b_{2} = 0
b1b2=−36b_{1} b_{2} = -36
The graph
05-20-15-10-510152002000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
b1 = -6
b1=−6b_{1} = -6 
b2 = 6
b2=6b_{2} = 6 
b2 = 6
Sum and product of roots [src] 
sum
-6 + 6
−6+6-6 + 6 
=
0
00 
product
-6*6
−36- 36 
=
-36
−36-36 
-36
Numerical answer [src] 
b1 = 6.0
b2 = -6.0
b2 = -6.0
    © Mister Exam – Calculator