x(x+1)=528

Simple and best practice solution for x(x+1)=528 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)=528 equation: 


Simplifying
x(x + 1) = 528

Reorder the terms:
x(1 + x) = 528
(1 * x + x * x) = 528
(1x + x2) = 528

Solving
1x + x2 = 528

Solving for variable 'x'.

Reorder the terms:
-528 + 1x + x2 = 528 + -528

Combine like terms: 528 + -528 = 0
-528 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '528' to each side of the equation.
-528 + 1x + 528 + x2 = 0 + 528

Reorder the terms:
-528 + 528 + 1x + x2 = 0 + 528

Combine like terms: -528 + 528 = 0
0 + 1x + x2 = 0 + 528
1x + x2 = 0 + 528

Combine like terms: 0 + 528 = 528
1x + x2 = 528

The x term is 1x.  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 = 528 + 0.25

Reorder the terms:
0.25 + x + x2 = 528 + 0.25

Combine like terms: 528 + 0.25 = 528.25
0.25 + x + x2 = 528.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 528.25

Calculate the square root of the right side: 22.983689869

Break this problem into two subproblems by setting 
(x + 0.5) equal to 22.983689869 and -22.983689869.


Subproblem 1
x + 0.5 = 22.983689869

Simplifying
x + 0.5 = 22.983689869

Reorder the terms:
0.5 + x = 22.983689869

Solving
0.5 + x = 22.983689869

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 = 22.983689869 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 22.983689869 + -0.5
x = 22.983689869 + -0.5

Combine like terms: 22.983689869 + -0.5 = 22.483689869
x = 22.483689869

Simplifying
x = 22.483689869


Subproblem 2
x + 0.5 = -22.983689869

Simplifying
x + 0.5 = -22.983689869

Reorder the terms:
0.5 + x = -22.983689869

Solving
0.5 + x = -22.983689869

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 = -22.983689869 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -22.983689869 + -0.5
x = -22.983689869 + -0.5

Combine like terms: -22.983689869 + -0.5 = -23.483689869
x = -23.483689869

Simplifying
x = -23.483689869


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.483689869, -23.483689869}

See similar equations:

| 32n^2-212n+120=0 | | 5-2z=7 | | 7-9g=61 | | a-8=-18 | | 3.2y-1.8=13 | | 20-47= | | 2(-2x+5)=50 | | 5n=20(4+2n) | | (2.8-4q)3.9= | | 3x=-3x-4 | | 3(h-6)=4h | | 5u+10=70 | | X^24x-81= | | 0.6x-1.5=13 | | 4(3t+4)-20=3+3t | | 6x-6=-5 | | 2(11+3n)=7x-26 | | -1.7(2.8-4q)3.9= | | 4.7a+8.2a-6.5a= | | -3n-(8-7)=n-(n+4) | | -7(9h)=378 | | 4(2t+5)-20=7t-6 | | 50x-25=2x^3-x^2 | | 8d-2d=36 | | c+2v+8=8+2v+v | | -12-6m=48 | | 0=t-17+4 | | 3f(3)=3x-7 | | -9+p-25=16 | | 0.3(4+x)=4.5 | | v^2+v-6=0 | | x^3-4x^2+x-4=0 |

Equations solver categories