Mister Exam

Other calculators

√8x-7=√3x+5 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] 
  _____         _____    
\/ 8*x  - 7 = \/ 3*x  + 5
8x−7=3x+5\sqrt{8 x} - 7 = \sqrt{3 x} + 5
Simplify
Detail solution
Given the equation
8x−7=3x+5\sqrt{8 x} - 7 = \sqrt{3 x} + 5
Transfer the right side of the equation left part with negative sign
x(−3+22)=12\sqrt{x} \left(- \sqrt{3} + 2 \sqrt{2}\right) = 12
We raise the equation sides to 2-th degree
x(−3+22)2=144x \left(- \sqrt{3} + 2 \sqrt{2}\right)^{2} = 144
x(−3+22)2=144x \left(- \sqrt{3} + 2 \sqrt{2}\right)^{2} = 144
Transfer the right side of the equation left part with negative sign
x(−3+22)2−144=0x \left(- \sqrt{3} + 2 \sqrt{2}\right)^{2} - 144 = 0
Expand brackets in the left part
-144 + x-sqrt+3 + 2*sqrt2)^2 = 0

Looking for similar summands in the left part:
-144 + x*(-sqrt(3) + 2*sqrt(2))^2 = 0

Move free summands (without x)
from left part to right part, we given:
x(−3+22)2=144x \left(- \sqrt{3} + 2 \sqrt{2}\right)^{2} = 144
Divide both parts of the equation by (-sqrt(3) + 2*sqrt(2))^2
x = 144 / ((-sqrt(3) + 2*sqrt(2))^2)

We get the answer: x = 1584/25 + 576*sqrt(6)/25

Because
x=12−3+22\sqrt{x} = \frac{12}{- \sqrt{3} + 2 \sqrt{2}}
and
x≥0\sqrt{x} \geq 0
then
12−3+22≥0\frac{12}{- \sqrt{3} + 2 \sqrt{2}} \geq 0
The final answer:
x1=576625+158425x_{1} = \frac{576 \sqrt{6}}{25} + \frac{1584}{25}
The graph
11011211411611812012212412612822.527.5
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
                  ___
     1584   576*\/ 6 
x1 = ---- + ---------
      25        25
x1=576625+158425x_{1} = \frac{576 \sqrt{6}}{25} + \frac{1584}{25} 
x1 = 576*sqrt(6)/25 + 1584/25
Sum and product of roots [src] 
sum
             ___
1584   576*\/ 6 
---- + ---------
 25        25
576625+158425\frac{576 \sqrt{6}}{25} + \frac{1584}{25} 
=
             ___
1584   576*\/ 6 
---- + ---------
 25        25
576625+158425\frac{576 \sqrt{6}}{25} + \frac{1584}{25} 
product
             ___
1584   576*\/ 6 
---- + ---------
 25        25
576625+158425\frac{576 \sqrt{6}}{25} + \frac{1584}{25} 
=
             ___
1584   576*\/ 6 
---- + ---------
 25        25
576625+158425\frac{576 \sqrt{6}}{25} + \frac{1584}{25} 
1584/25 + 576*sqrt(6)/25
Numerical answer [src] 
x1 = 119.796243673724
x1 = 119.796243673724
    © Mister Exam – Calculator