x^2+20x+40=0

Simple and best practice solution for x^2+20x+40=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+20x+40=0 equation: 


Simplifying
x2 + 20x + 40 = 0

Reorder the terms:
40 + 20x + x2 = 0

Solving
40 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + 20x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + 20x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + 20x + x2 = 0 + -40
20x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
20x + x2 = -40

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -40 + 100

Reorder the terms:
100 + 20x + x2 = -40 + 100

Combine like terms: -40 + 100 = 60
100 + 20x + x2 = 60

Factor a perfect square on the left side:
(x + 10)(x + 10) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(x + 10) equal to 7.745966692 and -7.745966692.


Subproblem 1
x + 10 = 7.745966692

Simplifying
x + 10 = 7.745966692

Reorder the terms:
10 + x = 7.745966692

Solving
10 + x = 7.745966692

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 7.745966692 + -10

Combine like terms: 10 + -10 = 0
0 + x = 7.745966692 + -10
x = 7.745966692 + -10

Combine like terms: 7.745966692 + -10 = -2.254033308
x = -2.254033308

Simplifying
x = -2.254033308


Subproblem 2
x + 10 = -7.745966692

Simplifying
x + 10 = -7.745966692

Reorder the terms:
10 + x = -7.745966692

Solving
10 + x = -7.745966692

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -7.745966692 + -10

Combine like terms: 10 + -10 = 0
0 + x = -7.745966692 + -10
x = -7.745966692 + -10

Combine like terms: -7.745966692 + -10 = -17.745966692
x = -17.745966692

Simplifying
x = -17.745966692


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.254033308, -17.745966692}

See similar equations:

| 5w^2-13w-6=0 | | 9z+5-6z=32-6z | | 3x+5=8-x | | 14-38=-6x | | -6x-9=-3 | | 4h-1=h+5 | | -7(x)=3x+6 | | 4x+3=7-x | | 5(2g+3)=5 | | 9x+13=6x+10 | | 40=-2(23-m)+3(m-3) | | 3(x)=2x+2 | | 6z-3z=5 | | 7x+5=5x+1 | | 39-4x=14x+15 | | 3(2-p)= | | 9-7x=99-28x | | 2e+24=5e | | -7u+9u=15-9 | | 3x+8=7x-8 | | 3a+1=9 | | 2(x)=x+4 | | 5x+7=9x+1 | | -2(x-3)=4(x+2)-9 | | 6x+5=13+14x | | 3a-42=3(a+4) | | -7x=-4x-6 | | -31-4x=5-10x | | 11b-6=27 | | 161-7x=38x+16 | | 2d=3 | | 5y-c=6y |

Equations solver categories