x^2+2013x+2014=0

Simple and best practice solution for x^2+2013x+2014=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 x^2+2013x+2014=0 equation: 


Simplifying
x2 + 2013x + 2014 = 0

Reorder the terms:
2014 + 2013x + x2 = 0

Solving
2014 + 2013x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2014' to each side of the equation.
2014 + 2013x + -2014 + x2 = 0 + -2014

Reorder the terms:
2014 + -2014 + 2013x + x2 = 0 + -2014

Combine like terms: 2014 + -2014 = 0
0 + 2013x + x2 = 0 + -2014
2013x + x2 = 0 + -2014

Combine like terms: 0 + -2014 = -2014
2013x + x2 = -2014

The x term is 2013x.  Take half its coefficient (1006.5).
Square it (1013042.25) and add it to both sides.

Add '1013042.25' to each side of the equation.
2013x + 1013042.25 + x2 = -2014 + 1013042.25

Reorder the terms:
1013042.25 + 2013x + x2 = -2014 + 1013042.25

Combine like terms: -2014 + 1013042.25 = 1011028.25
1013042.25 + 2013x + x2 = 1011028.25

Factor a perfect square on the left side:
(x + 1006.5)(x + 1006.5) = 1011028.25

Calculate the square root of the right side: 1005.499005469

Break this problem into two subproblems by setting 
(x + 1006.5) equal to 1005.499005469 and -1005.499005469.


Subproblem 1
x + 1006.5 = 1005.499005469

Simplifying
x + 1006.5 = 1005.499005469

Reorder the terms:
1006.5 + x = 1005.499005469

Solving
1006.5 + x = 1005.499005469

Solving for variable 'x'.

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

Add '-1006.5' to each side of the equation.
1006.5 + -1006.5 + x = 1005.499005469 + -1006.5

Combine like terms: 1006.5 + -1006.5 = 0.0
0.0 + x = 1005.499005469 + -1006.5
x = 1005.499005469 + -1006.5

Combine like terms: 1005.499005469 + -1006.5 = -1.000994531
x = -1.000994531

Simplifying
x = -1.000994531


Subproblem 2
x + 1006.5 = -1005.499005469

Simplifying
x + 1006.5 = -1005.499005469

Reorder the terms:
1006.5 + x = -1005.499005469

Solving
1006.5 + x = -1005.499005469

Solving for variable 'x'.

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

Add '-1006.5' to each side of the equation.
1006.5 + -1006.5 + x = -1005.499005469 + -1006.5

Combine like terms: 1006.5 + -1006.5 = 0.0
0.0 + x = -1005.499005469 + -1006.5
x = -1005.499005469 + -1006.5

Combine like terms: -1005.499005469 + -1006.5 = -2011.999005469
x = -2011.999005469

Simplifying
x = -2011.999005469


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.000994531, -2011.999005469}

See similar equations:

| X^2-7x+3y=6y+8x+64 | | 2x+5y-4z=40 | | 8(3x-6)=80 | | -11=1+6x | | 5q=q+48 | | R+9=-9 | | v+1.3=4.36 | | 63x-194x+143=0 | | 5c^2+16c+16=0 | | 4(x-5)-3(x+2)-13=-30 | | 2y=10-4x | | -3+2x+7=0 | | -24=2x-10 | | 6x-15+x+8=16 | | 4(x-5)-3(k+2)-13=-30 | | y-8.6=8.3 | | 25+-55+(85+65)= | | 2x^2+3=15 | | -6(2x+1)-x=46 | | 100-3x=0 | | 100-3=0 | | 3x-6=x-16 | | -4v-3v=14 | | (4+-3)(6+-1x)=0 | | 3x+2x=9x+16 | | 2x+3+x+1=90 | | 5(3+2x)-x=-12 | | -13x+8=-9x-8 | | (4a^4)-4a+7=0 | | 3x^7y^5+21x^5y^4+6xy= | | 13x+8=-9x-8 | | 5x+y=500 |

Equations solver categories