x^2+x+2+x+2-100=0

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Solution for x^2+x+2+x+2-100=0 equation:


Simplifying
x2 + x + 2 + x + 2 + -100 = 0

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

Combine like terms: 2 + 2 = 4
4 + -100 + x + x + x2 = 0

Combine like terms: 4 + -100 = -96
-96 + x + x + x2 = 0

Combine like terms: x + x = 2x
-96 + 2x + x2 = 0

Solving
-96 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + 2x + 96 + x2 = 0 + 96

Reorder the terms:
-96 + 96 + 2x + x2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + 2x + x2 = 0 + 96
2x + x2 = 0 + 96

Combine like terms: 0 + 96 = 96
2x + x2 = 96

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 = 96 + 1

Reorder the terms:
1 + 2x + x2 = 96 + 1

Combine like terms: 96 + 1 = 97
1 + 2x + x2 = 97

Factor a perfect square on the left side:
(x + 1)(x + 1) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(x + 1) equal to 9.848857802 and -9.848857802.

Subproblem 1

x + 1 = 9.848857802 Simplifying x + 1 = 9.848857802 Reorder the terms: 1 + x = 9.848857802 Solving 1 + x = 9.848857802 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 = 9.848857802 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.848857802 + -1 x = 9.848857802 + -1 Combine like terms: 9.848857802 + -1 = 8.848857802 x = 8.848857802 Simplifying x = 8.848857802

Subproblem 2

x + 1 = -9.848857802 Simplifying x + 1 = -9.848857802 Reorder the terms: 1 + x = -9.848857802 Solving 1 + x = -9.848857802 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 = -9.848857802 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.848857802 + -1 x = -9.848857802 + -1 Combine like terms: -9.848857802 + -1 = -10.848857802 x = -10.848857802 Simplifying x = -10.848857802

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.848857802, -10.848857802}

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