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Equation:
Equation 3(x+3)=2x+5
Equation (x-3)*(x+2)=0
Equation x^2-10*x-24=0
Equation 25x^2-1=0
Express {x} in terms of y where:
-17*x+18*y=10
-20*x-13*y=15
5*x+19*y=-3
-13*x-9*y=1
Identical expressions
four *cos(two *x)*cos(three *x)+ three = six *sin(two *x+ three *pi/ two)+ two *(-cos(three *x))
4 multiply by co sinus of e of (2 multiply by x) multiply by co sinus of e of (3 multiply by x) plus 3 equally 6 multiply by sinus of (2 multiply by x plus 3 multiply by Pi divide by 2) plus 2 multiply by ( minus co sinus of e of (3 multiply by x))
four multiply by co sinus of e of (two multiply by x) multiply by co sinus of e of (three multiply by x) plus three equally six multiply by sinus of (two multiply by x plus three multiply by Pi divide by two) plus two multiply by ( minus co sinus of e of (three multiply by x))
4cos(2x)cos(3x)+3=6sin(2x+3pi/2)+2(-cos(3x))
4cos2xcos3x+3=6sin2x+3pi/2+2-cos3x
4*cos(2*x)*cos(3*x)+3=6*sin(2*x+3*pi divide by 2)+2*(-cos(3*x))
Similar expressions
4*cos(2*x)*cos(3*x)+3=6*sin(2*x+3*pi/2)-2*(-cos(3*x))
4*cos(2*x)*cos(3*x)+3=6*sin(2*x+3*pi/2)+2*(cos(3*x))
4*cos(2*x)*cos(3*x)-3=6*sin(2*x+3*pi/2)+2*(-cos(3*x))
4*cos(2*x)*cos(3*x)+3=6*sin(2*x-3*pi/2)+2*(-cos(3*x))

4cos(2x)cos(3x)+3=6sin(2x+3pi/2)+2(-cos(3*x)) equation

The teacher will be very surprised to see your correct solution 😉

The solution

You have entered [src]

                               /      3*pi\                
4*cos(2*x)*cos(3*x) + 3 = 6*sin|2*x + ----| + 2*(-cos(3*x))
                               \       2  /

$$4 \cos{\left(2 x \right)} \cos{\left(3 x \right)} + 3 = 6 \sin{\left(2 x + \frac{3 \pi}{2} \right)} + 2 \left(- \cos{\left(3 x \right)}\right)$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

     -pi 
x1 = ----
      3

$$x_{1} = - \frac{\pi}{3}$$

     pi
x2 = --
     3

$$x_{2} = \frac{\pi}{3}$$

         /     /  ___\\         /     /  ___\\
     2*im\atanh\\/ 5 //   2*I*re\atanh\\/ 5 //
x3 = ------------------ - --------------------
             3                     3

$$x_{3} = \frac{2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3} - \frac{2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3}$$

           /     /  ___\\         /     /  ___\\
       2*im\atanh\\/ 5 //   2*I*re\atanh\\/ 5 //
x4 = - ------------------ + --------------------
               3                     3

$$x_{4} = - \frac{2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3} + \frac{2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3}$$

x4 = -2*im(atanh(sqrt(5)))/3 + 2*i*re(atanh(sqrt(5)))/3

Sum and product of roots [src]

sum

                /     /  ___\\         /     /  ___\\         /     /  ___\\         /     /  ___\\
  pi   pi   2*im\atanh\\/ 5 //   2*I*re\atanh\\/ 5 //     2*im\atanh\\/ 5 //   2*I*re\atanh\\/ 5 //
- -- + -- + ------------------ - -------------------- + - ------------------ + --------------------
  3    3            3                     3                       3                     3

$$\left(\left(- \frac{\pi}{3} + \frac{\pi}{3}\right) + \left(\frac{2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3} - \frac{2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3}\right)\right) + \left(- \frac{2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3} + \frac{2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3}\right)$$

$$0$$

product

        /    /     /  ___\\         /     /  ___\\\ /      /     /  ___\\         /     /  ___\\\
-pi  pi |2*im\atanh\\/ 5 //   2*I*re\atanh\\/ 5 //| |  2*im\atanh\\/ 5 //   2*I*re\atanh\\/ 5 //|
----*--*|------------------ - --------------------|*|- ------------------ + --------------------|
 3   3  \        3                     3          / \          3                     3          /

$$- \frac{\pi}{3} \frac{\pi}{3} \left(\frac{2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3} - \frac{2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3}\right) \left(- \frac{2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3} + \frac{2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3}\right)$$

                                               2
    2 /      /     /  ___\\     /     /  ___\\\ 
4*pi *\- I*re\atanh\\/ 5 // + im\atanh\\/ 5 /// 
------------------------------------------------
                       81

$$\frac{4 \pi^{2} \left(\operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)} - i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}\right)^{2}}{81}$$

4*pi^2*(-i*re(atanh(sqrt(5))) + im(atanh(sqrt(5))))^2/81

Numerical answer [src]

x1 = 30.3687289847013

x2 = 89.0117918517108

x3 = -83.7758040957278

x4 = 36.6519142918809

x5 = 10985.1023120523

x6 = 76.4454212373516

x7 = 32.4631240870945

x8 = 74.3510261349584

x9 = 105.766952670856

x10 = -5.23598775598299

x11 = 4.18879020478639

x12 = 80.634211442138

x13 = -96.342174710087

x14 = -76.4454212373516

x15 = 24.0855436775217

x16 = -55.5014702134197

x17 = -39.7935069454707

x18 = 2.0943951023932

x19 = -7.33038285837618

x20 = 112.050137978036

x21 = 83.7758040957278

x22 = -61.7846555205993

x23 = 68.0678408277789

x24 = -35.6047167406843

x25 = -41.8879020478639

x26 = -82.7286065445312

x27 = -85.870199198121

x28 = -79.5870138909414

x29 = -893.259511170698

x30 = -51.3126800086333

x31 = -45.0294947014537

x32 = 52.3598775598299

x33 = -42.9350995990605

x34 = 23.0383461263252

x35 = 11.5191730631626

x36 = -30.3687289847013

x37 = 93.2005820564972

x38 = 54.4542726622231

x39 = 85.870199198121

x40 = 13365.3823459222

x41 = -32.4631240870945

x42 = -49.2182849062401

x43 = -24.0855436775217

x44 = -48.1710873550435

x45 = -68.0678408277789

x46 = 1.0471975511966

x47 = 96.342174710087

x48 = -36.6519142918809

x49 = -11.5191730631626

x50 = 39.7935069454707

x51 = -52.3598775598299

x52 = -17.8023583703422

x53 = 82.7286065445312

x54 = 55.5014702134197

x55 = 38.7463093942741

x56 = 99.4837673636768

x57 = 92.1533845053006

x58 = -19.8967534727354

x59 = 61.7846555205993

x60 = 13.6135681655558

x61 = -57.5958653158129

x62 = -2.0943951023932

x63 = -26.1799387799149

x64 = -70.162235930172

x65 = 46.0766922526503

x66 = 17.8023583703422

x67 = 49.2182849062401

x68 = -90.0589894029074

x69 = 48.1710873550435

x70 = 41.8879020478639

x71 = 10.471975511966

x72 = -2040.98802728217

x73 = 70.162235930172

x74 = -92.1533845053006

x75 = -13.6135681655558

x76 = -225.147473507269

x77 = -38.7463093942741

x78 = 98.4365698124802

x79 = 57.5958653158129

x80 = -95.2949771588904

x81 = 90.0589894029074

x82 = -99.4837673636768

x83 = 5.23598775598299

x84 = -63.8790506229925

x85 = 19.8967534727354

x86 = -93.2005820564972

x87 = -33.5103216382911

x88 = -4.18879020478639

x89 = -117.286125734019

x90 = 63.8790506229925

x91 = -74.3510261349584

x92 = -46.0766922526503

x93 = 8.37758040957278

x94 = 45.0294947014537

x95 = 26.1799387799149

x96 = -77.4926187885482

x96 = -77.4926187885482

Other calculators

How to use it?

Identical expressions

Similar expressions

4*cos(2*x)*cos(3*x)+3=6*sin(2*x+3*pi/2)+2*(-cos(3*x)) equation

Numerical solution:

The solution

4cos(2x)cos(3x)+3=6sin(2x+3pi/2)+2(-cos(3*x)) equation