205=x(5x+4)

Simple and best practice solution for 205=x(5x+4) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 205=x(5x+4) equation: 


Simplifying
205 = x(5x + 4)

Reorder the terms:
205 = x(4 + 5x)
205 = (4 * x + 5x * x)
205 = (4x + 5x2)

Solving
205 = 4x + 5x2

Solving for variable 'x'.

Reorder the terms:
205 + -4x + -5x2 = 4x + -4x + 5x2 + -5x2

Combine like terms: 4x + -4x = 0
205 + -4x + -5x2 = 0 + 5x2 + -5x2
205 + -4x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
205 + -4x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-41 + 0.8x + x2 = 0

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + 0.8x + 41 + x2 = 0 + 41

Reorder the terms:
-41 + 41 + 0.8x + x2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + 0.8x + x2 = 0 + 41
0.8x + x2 = 0 + 41

Combine like terms: 0 + 41 = 41
0.8x + x2 = 41

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 41 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 41 + 0.16

Combine like terms: 41 + 0.16 = 41.16
0.16 + 0.8x + x2 = 41.16

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 41.16

Calculate the square root of the right side: 6.415605973

Break this problem into two subproblems by setting 
(x + 0.4) equal to 6.415605973 and -6.415605973.


Subproblem 1
x + 0.4 = 6.415605973

Simplifying
x + 0.4 = 6.415605973

Reorder the terms:
0.4 + x = 6.415605973

Solving
0.4 + x = 6.415605973

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 6.415605973 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 6.415605973 + -0.4
x = 6.415605973 + -0.4

Combine like terms: 6.415605973 + -0.4 = 6.015605973
x = 6.015605973

Simplifying
x = 6.015605973


Subproblem 2
x + 0.4 = -6.415605973

Simplifying
x + 0.4 = -6.415605973

Reorder the terms:
0.4 + x = -6.415605973

Solving
0.4 + x = -6.415605973

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -6.415605973 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -6.415605973 + -0.4
x = -6.415605973 + -0.4

Combine like terms: -6.415605973 + -0.4 = -6.815605973
x = -6.815605973

Simplifying
x = -6.815605973


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.015605973, -6.815605973}

See similar equations:

| (yx+1)dx+(1-xy)dy=0 | | 0.25x+0.4(75-x)=24 | | 0.25+0.4(75-x)=24 | | (0.45)-(-0.09)= | | (3x+1)(5x-7)=0 | | 2x+1=5x+2-3x-6 | | 2(2x-4.9)=8x-9.8 | | (6)/(z-4)=5/3 | | (-6.9)-(-7.3)= | | 13lnx-7=0 | | 13x-1/3x+9=4 | | (-6.0)+(-3.2)= | | 15-27=15 | | (7.5)-(12.3)= | | X-60=5x | | (-0.25)+(0.41)= | | (-18.1)+(10.9)= | | -10=-14v+14v+3 | | 10(1+3b)=-20+3b | | 15=(2.5x)/2 | | 5.7+0.8x=0.9 | | (-5.5)-(-8.7)= | | 3(4x-2.4)=5x-7.2 | | 20/2(5*5)=x | | 2k^2+6=4k | | (-3.8)+(0.13)= | | 3y/5=37-4 | | 4.7+0.05x=5.09 | | 7.1=10x+1.5 | | Ln(x-1)+Ln(3)=Lnx | | (x+1)+(x-1)=45 | | f=4.135135 |

Equations solver categories