2x^2+x-405=0

Simple and best practice solution for 2x^2+x-405=0 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 2x^2+x-405=0 equation: 


Simplifying
2x2 + x + -405 = 0

Reorder the terms:
-405 + x + 2x2 = 0

Solving
-405 + x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-202.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '202.5' to each side of the equation.
-202.5 + 0.5x + 202.5 + x2 = 0 + 202.5

Reorder the terms:
-202.5 + 202.5 + 0.5x + x2 = 0 + 202.5

Combine like terms: -202.5 + 202.5 = 0.0
0.0 + 0.5x + x2 = 0 + 202.5
0.5x + x2 = 0 + 202.5

Combine like terms: 0 + 202.5 = 202.5
0.5x + x2 = 202.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5x + 0.25 + x2 = 202.5 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = 202.5 + 0.25

Combine like terms: 202.5 + 0.25 = 202.75
0.25 + 0.5x + x2 = 202.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 202.75

Calculate the square root of the right side: 14.239030866

Break this problem into two subproblems by setting 
(x + 0.5) equal to 14.239030866 and -14.239030866.


Subproblem 1
x + 0.5 = 14.239030866

Simplifying
x + 0.5 = 14.239030866

Reorder the terms:
0.5 + x = 14.239030866

Solving
0.5 + x = 14.239030866

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 14.239030866 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 14.239030866 + -0.5
x = 14.239030866 + -0.5

Combine like terms: 14.239030866 + -0.5 = 13.739030866
x = 13.739030866

Simplifying
x = 13.739030866


Subproblem 2
x + 0.5 = -14.239030866

Simplifying
x + 0.5 = -14.239030866

Reorder the terms:
0.5 + x = -14.239030866

Solving
0.5 + x = -14.239030866

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -14.239030866 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -14.239030866 + -0.5
x = -14.239030866 + -0.5

Combine like terms: -14.239030866 + -0.5 = -14.739030866
x = -14.739030866

Simplifying
x = -14.739030866


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.739030866, -14.739030866}

See similar equations:

| n-3/8=1/8 | | 5x-3=9+8x | | xz+y=1+z | | e^7(x)=11 | | e^7x=11 | | 51=x+(x+1)+(x-1) | | 7x+8-2x+5=33 | | 5(c+2)+7c= | | 42=2(l+w) | | 2(y+3)= | | 6x^2+15x-8x-20=0 | | 8y+y-2y-8y= | | (-2x)*(-7x)= | | 10x-12=3x+5 | | 7z-10z= | | 2n-3n= | | 5(x-y)= | | 7x*5x*3x= | | Log(3x-5)=20 | | 3t^2+9-2=0 | | 5(9x-6x)= | | -(x+2)-2x=2(x+1) | | 12m^2+20m-8=0 | | (5y-9)(3-y)=0 | | 7x(3-2)= | | X(3+6)= | | 2x^5+7x^4-2x^3-34x^2=-8x | | 2x+12=-2x+8 | | 2x+12=-2+8 | | x^2+11=11 | | 8n-2n-3=12 | | 22-0.5-p=0 |

Equations solver categories