x(x+1)+(x+2)+(x+3)+(x+4)=28

Simple and best practice solution for x(x+1)+(x+2)+(x+3)+(x+4)=28 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(x+1)+(x+2)+(x+3)+(x+4)=28 equation:


Simplifying
x(x + 1) + (x + 2) + (x + 3) + (x + 4) = 28

Reorder the terms:
x(1 + x) + (x + 2) + (x + 3) + (x + 4) = 28
(1 * x + x * x) + (x + 2) + (x + 3) + (x + 4) = 28
(1x + x2) + (x + 2) + (x + 3) + (x + 4) = 28

Reorder the terms:
1x + x2 + (2 + x) + (x + 3) + (x + 4) = 28

Remove parenthesis around (2 + x)
1x + x2 + 2 + x + (x + 3) + (x + 4) = 28

Reorder the terms:
1x + x2 + 2 + x + (3 + x) + (x + 4) = 28

Remove parenthesis around (3 + x)
1x + x2 + 2 + x + 3 + x + (x + 4) = 28

Reorder the terms:
1x + x2 + 2 + x + 3 + x + (4 + x) = 28

Remove parenthesis around (4 + x)
1x + x2 + 2 + x + 3 + x + 4 + x = 28

Reorder the terms:
2 + 3 + 4 + 1x + x + x + x + x2 = 28

Combine like terms: 2 + 3 = 5
5 + 4 + 1x + x + x + x + x2 = 28

Combine like terms: 5 + 4 = 9
9 + 1x + x + x + x + x2 = 28

Combine like terms: 1x + x = 2x
9 + 2x + x + x + x2 = 28

Combine like terms: 2x + x = 3x
9 + 3x + x + x2 = 28

Combine like terms: 3x + x = 4x
9 + 4x + x2 = 28

Solving
9 + 4x + x2 = 28

Solving for variable 'x'.

Reorder the terms:
9 + -28 + 4x + x2 = 28 + -28

Combine like terms: 9 + -28 = -19
-19 + 4x + x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-19 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 4x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + 4x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 4x + x2 = 0 + 19
4x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
4x + x2 = 19

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 19 + 4

Reorder the terms:
4 + 4x + x2 = 19 + 4

Combine like terms: 19 + 4 = 23
4 + 4x + x2 = 23

Factor a perfect square on the left side:
(x + 2)(x + 2) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(x + 2) equal to 4.795831523 and -4.795831523.

Subproblem 1

x + 2 = 4.795831523 Simplifying x + 2 = 4.795831523 Reorder the terms: 2 + x = 4.795831523 Solving 2 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.795831523 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.795831523 + -2 x = 4.795831523 + -2 Combine like terms: 4.795831523 + -2 = 2.795831523 x = 2.795831523 Simplifying x = 2.795831523

Subproblem 2

x + 2 = -4.795831523 Simplifying x + 2 = -4.795831523 Reorder the terms: 2 + x = -4.795831523 Solving 2 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.795831523 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.795831523 + -2 x = -4.795831523 + -2 Combine like terms: -4.795831523 + -2 = -6.795831523 x = -6.795831523 Simplifying x = -6.795831523

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.795831523, -6.795831523}

See similar equations:

| 5x+20=5-3x+7 | | 3(r^2+2)=33 | | 3x(5x+2)=9x-12 | | 10b-25-36=46-1 | | 2(x-3)-3(2x+1)=4(1-3x) | | 20+3y-3=13y-11-3y | | 7[x+2]=2x-11 | | 5(r^2-1)=120 | | 2r^2-1=7 | | (4x+14)+(2x-10)=180 | | 7-4x=x+5 | | 2[x-3]=4[x+6] | | 3r^2+3=30 | | 75+4=150+x | | 3*4-3y=12 | | 8x+5y= -84 | | 9(4x+3)= | | 75x+4x=150+x | | 3(4r-5)=45 | | -3a-12=15 | | 3*3y=12 | | 5(2r+3)=95 | | -x+4y=-0.5 | | 7m-2(m-3)=-14 | | 3*-3y=12 | | 18=8-5 | | -2(3r-4)=32 | | -3(4r+2)=18 | | 4r+2=34 | | 3x+2y=12xy | | 4x^2+60x-32=0 | | 2(x+1)+x(x+2)+(x+3)+(x+4)=28 |

Equations solver categories