100=x(x+2)

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Solution for 100=x(x+2) equation:


Simplifying
100 = x(x + 2)

Reorder the terms:
100 = x(2 + x)
100 = (2 * x + x * x)
100 = (2x + x2)

Solving
100 = 2x + x2

Solving for variable 'x'.

Reorder the terms:
100 + -2x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
100 + -2x + -1x2 = 0 + x2 + -1x2
100 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
100 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-100 + 2x + x2 = 0

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 2x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 2x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 2x + x2 = 0 + 100
2x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
2x + x2 = 100

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 100 + 1

Reorder the terms:
1 + 2x + x2 = 100 + 1

Combine like terms: 100 + 1 = 101
1 + 2x + x2 = 101

Factor a perfect square on the left side:
(x + 1)(x + 1) = 101

Calculate the square root of the right side: 10.049875621

Break this problem into two subproblems by setting 
(x + 1) equal to 10.049875621 and -10.049875621.

Subproblem 1

x + 1 = 10.049875621 Simplifying x + 1 = 10.049875621 Reorder the terms: 1 + x = 10.049875621 Solving 1 + x = 10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 10.049875621 + -1 Combine like terms: 1 + -1 = 0 0 + x = 10.049875621 + -1 x = 10.049875621 + -1 Combine like terms: 10.049875621 + -1 = 9.049875621 x = 9.049875621 Simplifying x = 9.049875621

Subproblem 2

x + 1 = -10.049875621 Simplifying x + 1 = -10.049875621 Reorder the terms: 1 + x = -10.049875621 Solving 1 + x = -10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -10.049875621 + -1 Combine like terms: 1 + -1 = 0 0 + x = -10.049875621 + -1 x = -10.049875621 + -1 Combine like terms: -10.049875621 + -1 = -11.049875621 x = -11.049875621 Simplifying x = -11.049875621

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.049875621, -11.049875621}

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