Mister Exam

Other calculators

sqrt(14+5*x)=x

sqrt(14+5*x)=x 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] 
  __________    
\/ 14 + 5*x  = x
5x+14=x\sqrt{5 x + 14} = x
Simplify
Detail solution
Given the equation
5x+14=x\sqrt{5 x + 14} = x
5x+14=x\sqrt{5 x + 14} = x
We raise the equation sides to 2-th degree
5x+14=x25 x + 14 = x^{2}
5x+14=x25 x + 14 = x^{2}
Transfer the right side of the equation left part with negative sign
−x2+5x+14=0- x^{2} + 5 x + 14 = 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=5b = 5
c=14c = 14
, then
D = b^2 - 4 * a * c = 

(5)^2 - 4 * (-1) * (14) = 81

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

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

or
x1=−2x_{1} = -2
x2=7x_{2} = 7

Because
5x+14=x\sqrt{5 x + 14} = x
and
5x+14≥0\sqrt{5 x + 14} \geq 0
then
x≥0x \geq 0
or
0≤x0 \leq x
x<∞x < \infty
The final answer:
x2=7x_{2} = 7
The graph
02468-210121416-2020
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 7
x1=7x_{1} = 7 
x1 = 7
Sum and product of roots [src] 
sum
7
77 
=
7
77 
product
7
77 
=
7
77 
7
Numerical answer [src] 
x1 = 7.0
x1 = 7.0
The graph
sqrt(14+5*x)=x equation
    © Mister Exam – Calculator