x^2+2x-1624=0

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Solution for x^2+2x-1624=0 equation:


Simplifying
x2 + 2x + -1624 = 0

Reorder the terms:
-1624 + 2x + x2 = 0

Solving
-1624 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1624' to each side of the equation.
-1624 + 2x + 1624 + x2 = 0 + 1624

Reorder the terms:
-1624 + 1624 + 2x + x2 = 0 + 1624

Combine like terms: -1624 + 1624 = 0
0 + 2x + x2 = 0 + 1624
2x + x2 = 0 + 1624

Combine like terms: 0 + 1624 = 1624
2x + x2 = 1624

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 = 1624 + 1

Reorder the terms:
1 + 2x + x2 = 1624 + 1

Combine like terms: 1624 + 1 = 1625
1 + 2x + x2 = 1625

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1625

Calculate the square root of the right side: 40.311288741

Break this problem into two subproblems by setting 
(x + 1) equal to 40.311288741 and -40.311288741.

Subproblem 1

x + 1 = 40.311288741 Simplifying x + 1 = 40.311288741 Reorder the terms: 1 + x = 40.311288741 Solving 1 + x = 40.311288741 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 = 40.311288741 + -1 Combine like terms: 1 + -1 = 0 0 + x = 40.311288741 + -1 x = 40.311288741 + -1 Combine like terms: 40.311288741 + -1 = 39.311288741 x = 39.311288741 Simplifying x = 39.311288741

Subproblem 2

x + 1 = -40.311288741 Simplifying x + 1 = -40.311288741 Reorder the terms: 1 + x = -40.311288741 Solving 1 + x = -40.311288741 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 = -40.311288741 + -1 Combine like terms: 1 + -1 = 0 0 + x = -40.311288741 + -1 x = -40.311288741 + -1 Combine like terms: -40.311288741 + -1 = -41.311288741 x = -41.311288741 Simplifying x = -41.311288741

Solution

The solution to the problem is based on the solutions from the subproblems. x = {39.311288741, -41.311288741}

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