x^2+2x-685=0

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Solution for x^2+2x-685=0 equation:


Simplifying
x2 + 2x + -685 = 0

Reorder the terms:
-685 + 2x + x2 = 0

Solving
-685 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '685' to each side of the equation.
-685 + 2x + 685 + x2 = 0 + 685

Reorder the terms:
-685 + 685 + 2x + x2 = 0 + 685

Combine like terms: -685 + 685 = 0
0 + 2x + x2 = 0 + 685
2x + x2 = 0 + 685

Combine like terms: 0 + 685 = 685
2x + x2 = 685

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 = 685 + 1

Reorder the terms:
1 + 2x + x2 = 685 + 1

Combine like terms: 685 + 1 = 686
1 + 2x + x2 = 686

Factor a perfect square on the left side:
(x + 1)(x + 1) = 686

Calculate the square root of the right side: 26.191601707

Break this problem into two subproblems by setting 
(x + 1) equal to 26.191601707 and -26.191601707.

Subproblem 1

x + 1 = 26.191601707 Simplifying x + 1 = 26.191601707 Reorder the terms: 1 + x = 26.191601707 Solving 1 + x = 26.191601707 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 = 26.191601707 + -1 Combine like terms: 1 + -1 = 0 0 + x = 26.191601707 + -1 x = 26.191601707 + -1 Combine like terms: 26.191601707 + -1 = 25.191601707 x = 25.191601707 Simplifying x = 25.191601707

Subproblem 2

x + 1 = -26.191601707 Simplifying x + 1 = -26.191601707 Reorder the terms: 1 + x = -26.191601707 Solving 1 + x = -26.191601707 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 = -26.191601707 + -1 Combine like terms: 1 + -1 = 0 0 + x = -26.191601707 + -1 x = -26.191601707 + -1 Combine like terms: -26.191601707 + -1 = -27.191601707 x = -27.191601707 Simplifying x = -27.191601707

Solution

The solution to the problem is based on the solutions from the subproblems. x = {25.191601707, -27.191601707}

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