x(x+1)=1050

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Solution for x(x+1)=1050 equation:


Simplifying
x(x + 1) = 1050

Reorder the terms:
x(1 + x) = 1050
(1 * x + x * x) = 1050
(1x + x2) = 1050

Solving
1x + x2 = 1050

Solving for variable 'x'.

Reorder the terms:
-1050 + 1x + x2 = 1050 + -1050

Combine like terms: 1050 + -1050 = 0
-1050 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1050' to each side of the equation.
-1050 + 1x + 1050 + x2 = 0 + 1050

Reorder the terms:
-1050 + 1050 + 1x + x2 = 0 + 1050

Combine like terms: -1050 + 1050 = 0
0 + 1x + x2 = 0 + 1050
1x + x2 = 0 + 1050

Combine like terms: 0 + 1050 = 1050
1x + x2 = 1050

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 = 1050 + 0.25

Reorder the terms:
0.25 + x + x2 = 1050 + 0.25

Combine like terms: 1050 + 0.25 = 1050.25
0.25 + x + x2 = 1050.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1050.25

Calculate the square root of the right side: 32.407560846

Break this problem into two subproblems by setting 
(x + 0.5) equal to 32.407560846 and -32.407560846.

Subproblem 1

x + 0.5 = 32.407560846 Simplifying x + 0.5 = 32.407560846 Reorder the terms: 0.5 + x = 32.407560846 Solving 0.5 + x = 32.407560846 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 = 32.407560846 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 32.407560846 + -0.5 x = 32.407560846 + -0.5 Combine like terms: 32.407560846 + -0.5 = 31.907560846 x = 31.907560846 Simplifying x = 31.907560846

Subproblem 2

x + 0.5 = -32.407560846 Simplifying x + 0.5 = -32.407560846 Reorder the terms: 0.5 + x = -32.407560846 Solving 0.5 + x = -32.407560846 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 = -32.407560846 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -32.407560846 + -0.5 x = -32.407560846 + -0.5 Combine like terms: -32.407560846 + -0.5 = -32.907560846 x = -32.907560846 Simplifying x = -32.907560846

Solution

The solution to the problem is based on the solutions from the subproblems. x = {31.907560846, -32.907560846}

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