x^2+2x=2.616

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Solution for x^2+2x=2.616 equation:


Simplifying
x2 + 2x = 2.616

Reorder the terms:
2x + x2 = 2.616

Solving
2x + x2 = 2.616

Solving for variable 'x'.

Reorder the terms:
-2.616 + 2x + x2 = 2.616 + -2.616

Combine like terms: 2.616 + -2.616 = 0.000
-2.616 + 2x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '2.616' to each side of the equation.
-2.616 + 2x + 2.616 + x2 = 0.000 + 2.616

Reorder the terms:
-2.616 + 2.616 + 2x + x2 = 0.000 + 2.616

Combine like terms: -2.616 + 2.616 = 0.000
0.000 + 2x + x2 = 0.000 + 2.616
2x + x2 = 0.000 + 2.616

Combine like terms: 0.000 + 2.616 = 2.616
2x + x2 = 2.616

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 = 2.616 + 1

Reorder the terms:
1 + 2x + x2 = 2.616 + 1

Combine like terms: 2.616 + 1 = 3.616
1 + 2x + x2 = 3.616

Factor a perfect square on the left side:
(x + 1)(x + 1) = 3.616

Calculate the square root of the right side: 1.901578292

Break this problem into two subproblems by setting 
(x + 1) equal to 1.901578292 and -1.901578292.

Subproblem 1

x + 1 = 1.901578292 Simplifying x + 1 = 1.901578292 Reorder the terms: 1 + x = 1.901578292 Solving 1 + x = 1.901578292 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 = 1.901578292 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.901578292 + -1 x = 1.901578292 + -1 Combine like terms: 1.901578292 + -1 = 0.901578292 x = 0.901578292 Simplifying x = 0.901578292

Subproblem 2

x + 1 = -1.901578292 Simplifying x + 1 = -1.901578292 Reorder the terms: 1 + x = -1.901578292 Solving 1 + x = -1.901578292 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 = -1.901578292 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.901578292 + -1 x = -1.901578292 + -1 Combine like terms: -1.901578292 + -1 = -2.901578292 x = -2.901578292 Simplifying x = -2.901578292

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.901578292, -2.901578292}

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