10x(x+1)=110

Simple and best practice solution for 10x(x+1)=110 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 10x(x+1)=110 equation: 


Simplifying
10x(x + 1) = 110

Reorder the terms:
10x(1 + x) = 110
(1 * 10x + x * 10x) = 110
(10x + 10x2) = 110

Solving
10x + 10x2 = 110

Solving for variable 'x'.

Reorder the terms:
-110 + 10x + 10x2 = 110 + -110

Combine like terms: 110 + -110 = 0
-110 + 10x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-11 + x + x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-11 + x + x2)' equal to zero and attempt to solve:

Simplifying
-11 + x + x2 = 0

Solving
-11 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + x + x2 = 0 + 11
x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
x + x2 = 11

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.
x + 0.25 + x2 = 11 + 0.25

Reorder the terms:
0.25 + x + x2 = 11 + 0.25

Combine like terms: 11 + 0.25 = 11.25
0.25 + x + x2 = 11.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
x + 0.5 = 3.354101966

Simplifying
x + 0.5 = 3.354101966

Reorder the terms:
0.5 + x = 3.354101966

Solving
0.5 + x = 3.354101966

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 = 3.354101966 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.354101966 + -0.5
x = 3.354101966 + -0.5

Combine like terms: 3.354101966 + -0.5 = 2.854101966
x = 2.854101966

Simplifying
x = 2.854101966


Subproblem 2
x + 0.5 = -3.354101966

Simplifying
x + 0.5 = -3.354101966

Reorder the terms:
0.5 + x = -3.354101966

Solving
0.5 + x = -3.354101966

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 = -3.354101966 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.354101966 + -0.5
x = -3.354101966 + -0.5

Combine like terms: -3.354101966 + -0.5 = -3.854101966
x = -3.854101966

Simplifying
x = -3.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.854101966, -3.854101966}
Solution
x = {2.854101966, -3.854101966}

See similar equations:

| 2/9m=8/27 | | 10-2x=-30 | | t-118=84 | | 2K+4=2(k+5)-6 | | 11x-(2-x)=15 | | 7(x+6)=4 | | X-2/x=9/10 | | 4/9x=3/5 | | x^2+4x+187=0 | | a-2b+3c-5=0 | | 6x-2(-3x-2)=154 | | 6/x-4=2/x-2 | | n+2n+2n+2=97 | | 3w+4=43 | | d-56=3 | | 7x-11x-1=-122 | | 1/4m-4=36 | | 63×4/9 | | 33=j-18 | | 4/x=27/108 | | 4/10=-p/3 | | 80/x=15/8 | | 4y+14+3x+7y=180 | | 15+k=15 | | -5+2u=-19 | | f(x)=3x^2+18x-8 | | y=15x+50 | | P(x)=x^4-9x^2+13 | | 3x-4(3x-2)=10(x+2) | | (9x+11)(7x+13)=0 | | P(30)=95000x+200000 | | 72x^3+6x^2-444x=0 |

Equations solver categories