3.35=x^2+2x

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Solution for 3.35=x^2+2x equation:


Simplifying
3.35 = x2 + 2x

Reorder the terms:
3.35 = 2x + x2

Solving
3.35 = 2x + x2

Solving for variable 'x'.

Reorder the terms:
3.35 + -2x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
3.35 + -2x + -1x2 = 0 + x2 + -1x2
3.35 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3.35 + -2x + -1x2 = 0

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

Divide each side by '-1'.
-3.35 + 2x + x2 = 0

Move the constant term to the right:

Add '3.35' to each side of the equation.
-3.35 + 2x + 3.35 + x2 = 0 + 3.35

Reorder the terms:
-3.35 + 3.35 + 2x + x2 = 0 + 3.35

Combine like terms: -3.35 + 3.35 = 0.00
0.00 + 2x + x2 = 0 + 3.35
2x + x2 = 0 + 3.35

Combine like terms: 0 + 3.35 = 3.35
2x + x2 = 3.35

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 = 3.35 + 1

Reorder the terms:
1 + 2x + x2 = 3.35 + 1

Combine like terms: 3.35 + 1 = 4.35
1 + 2x + x2 = 4.35

Factor a perfect square on the left side:
(x + 1)(x + 1) = 4.35

Calculate the square root of the right side: 2.085665361

Break this problem into two subproblems by setting 
(x + 1) equal to 2.085665361 and -2.085665361.

Subproblem 1

x + 1 = 2.085665361 Simplifying x + 1 = 2.085665361 Reorder the terms: 1 + x = 2.085665361 Solving 1 + x = 2.085665361 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 = 2.085665361 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.085665361 + -1 x = 2.085665361 + -1 Combine like terms: 2.085665361 + -1 = 1.085665361 x = 1.085665361 Simplifying x = 1.085665361

Subproblem 2

x + 1 = -2.085665361 Simplifying x + 1 = -2.085665361 Reorder the terms: 1 + x = -2.085665361 Solving 1 + x = -2.085665361 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 = -2.085665361 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.085665361 + -1 x = -2.085665361 + -1 Combine like terms: -2.085665361 + -1 = -3.085665361 x = -3.085665361 Simplifying x = -3.085665361

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.085665361, -3.085665361}

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