Mister Exam

Other calculators

x^2=15

x^2=15 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  = 15
x2=15x^{2} = 15
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
x2=15x^{2} = 15
to
x2−15=0x^{2} - 15 = 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=1a = 1
b=0b = 0
c=−15c = -15
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (-15) = 60

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

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

or
x1=15x_{1} = \sqrt{15}
x2=−15x_{2} = - \sqrt{15}
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=−15q = -15
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=0x_{1} + x_{2} = 0
x1x2=−15x_{1} x_{2} = -15
The graph
05-20-15-10-51015200200
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
        ____
x1 = -\/ 15
x1=−15x_{1} = - \sqrt{15} 
       ____
x2 = \/ 15
x2=15x_{2} = \sqrt{15} 
x2 = sqrt(15)
Sum and product of roots [src] 
sum
    ____     ____
- \/ 15  + \/ 15
−15+15- \sqrt{15} + \sqrt{15} 
=
0
00 
product
   ____   ____
-\/ 15 *\/ 15
−1515- \sqrt{15} \sqrt{15} 
=
-15
−15-15 
-15
Numerical answer [src] 
x1 = 3.87298334620742
x2 = -3.87298334620742
x2 = -3.87298334620742
The graph
x^2=15 equation
    © Mister Exam – Calculator