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sqrt(4*x^2+1250^2)*(1/3500)=x

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  • Identical expressions

  • sqrt(four *x^ two + one thousand, two hundred and fifty ^ two)*(one / three thousand, five hundred)=x
  • square root of (4 multiply by x squared plus 1250 squared ) multiply by (1 divide by 3500) equally x
  • square root of (four multiply by x to the power of two plus one thousand, two hundred and fifty to the power of two) multiply by (one divide by three thousand, five hundred) equally x
  • √(4*x^2+1250^2)*(1/3500)=x
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  • sqrt(4*x to the power of 2+1250 to the power of 2)*(1/3500)=x
  • sqrt(4x^2+1250^2)(1/3500)=x
  • sqrt(4x2+12502)(1/3500)=x
  • sqrt4x2+125021/3500=x
  • sqrt4x^2+1250^21/3500=x
  • sqrt(4*x^2+1250^2)*(1 divide by 3500)=x

  • Similar expressions

  • sqrt(4*x^2-1250^2)*(1/3500)=x

sqrt(4*x^2+1250^2)*(1/3500)=x equation

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Numerical solution:

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The solution

You have entered [src] 
   ______________           
  /    2       2            
\/  4*x  + 1250  *1/3500 = x
$$\sqrt{4 x^{2} + 1250^{2}} \cdot \frac{1}{3500} = x$$
Simplify
Detail solution
Given the equation
$$\sqrt{4 x^{2} + 1250^{2}} \cdot \frac{1}{3500} = x$$
$$\frac{\sqrt{4 x^{2} + 1562500}}{3500} = x$$
We raise the equation sides to 2-th degree
$$\frac{x^{2}}{3062500} + \frac{25}{196} = x^{2}$$
$$\frac{x^{2}}{3062500} + \frac{25}{196} = x^{2}$$
Transfer the right side of the equation left part with negative sign
$$- \frac{3062499 x^{2}}{3062500} + \frac{25}{196} = 0$$
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:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = - \frac{3062499}{3062500}$$
$$b = 0$$
$$c = \frac{25}{196}$$
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (-3062499/3062500) * (25/196) = 3062499/6002500

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

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

or
$$x_{1} = - \frac{625 \sqrt{3062499}}{3062499}$$
Simplify
$$x_{2} = \frac{625 \sqrt{3062499}}{3062499}$$
Simplify

Because
$$\sqrt{4 x^{2} + 1562500} = 3500 x$$
and
$$\sqrt{4 x^{2} + 1562500} \geq 0$$
then
$$3500 x \geq 0$$
or
$$0 \leq x$$
$$x < \infty$$
The final answer:
$$x_{2} = \frac{625 \sqrt{3062499}}{3062499}$$
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
           _________
     625*\/ 3062499 
x1 = ---------------
         3062499
$$x_{1} = \frac{625 \sqrt{3062499}}{3062499}$$
Simplify
Sum and product of roots [src] 
sum
          _________
    625*\/ 3062499 
0 + ---------------
        3062499
$$0 + \frac{625 \sqrt{3062499}}{3062499}$$ 
=
      _________
625*\/ 3062499 
---------------
    3062499
$$\frac{625 \sqrt{3062499}}{3062499}$$ 
product
        _________
  625*\/ 3062499 
1*---------------
      3062499
$$1 \cdot \frac{625 \sqrt{3062499}}{3062499}$$ 
=
      _________
625*\/ 3062499 
---------------
    3062499
$$\frac{625 \sqrt{3062499}}{3062499}$$ 
625*sqrt(3062499)/3062499
Numerical answer [src] 
x1 = 0.357142915451909
x1 = 0.357142915451909
The graph
sqrt(4*x^2+1250^2)*(1/3500)=x equation
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