x^2+2x-280=0

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Solution for x^2+2x-280=0 equation:


Simplifying
x2 + 2x + -280 = 0

Reorder the terms:
-280 + 2x + x2 = 0

Solving
-280 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '280' to each side of the equation.
-280 + 2x + 280 + x2 = 0 + 280

Reorder the terms:
-280 + 280 + 2x + x2 = 0 + 280

Combine like terms: -280 + 280 = 0
0 + 2x + x2 = 0 + 280
2x + x2 = 0 + 280

Combine like terms: 0 + 280 = 280
2x + x2 = 280

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 = 280 + 1

Reorder the terms:
1 + 2x + x2 = 280 + 1

Combine like terms: 280 + 1 = 281
1 + 2x + x2 = 281

Factor a perfect square on the left side:
(x + 1)(x + 1) = 281

Calculate the square root of the right side: 16.763054614

Break this problem into two subproblems by setting 
(x + 1) equal to 16.763054614 and -16.763054614.

Subproblem 1

x + 1 = 16.763054614 Simplifying x + 1 = 16.763054614 Reorder the terms: 1 + x = 16.763054614 Solving 1 + x = 16.763054614 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 = 16.763054614 + -1 Combine like terms: 1 + -1 = 0 0 + x = 16.763054614 + -1 x = 16.763054614 + -1 Combine like terms: 16.763054614 + -1 = 15.763054614 x = 15.763054614 Simplifying x = 15.763054614

Subproblem 2

x + 1 = -16.763054614 Simplifying x + 1 = -16.763054614 Reorder the terms: 1 + x = -16.763054614 Solving 1 + x = -16.763054614 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 = -16.763054614 + -1 Combine like terms: 1 + -1 = 0 0 + x = -16.763054614 + -1 x = -16.763054614 + -1 Combine like terms: -16.763054614 + -1 = -17.763054614 x = -17.763054614 Simplifying x = -17.763054614

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.763054614, -17.763054614}

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