x^2+4x-280=0

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Solution for x^2+4x-280=0 equation:


Simplifying
x2 + 4x + -280 = 0

Reorder the terms:
-280 + 4x + x2 = 0

Solving
-280 + 4x + 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 + 4x + 280 + x2 = 0 + 280

Reorder the terms:
-280 + 280 + 4x + x2 = 0 + 280

Combine like terms: -280 + 280 = 0
0 + 4x + x2 = 0 + 280
4x + x2 = 0 + 280

Combine like terms: 0 + 280 = 280
4x + x2 = 280

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 280 + 4

Reorder the terms:
4 + 4x + x2 = 280 + 4

Combine like terms: 280 + 4 = 284
4 + 4x + x2 = 284

Factor a perfect square on the left side:
(x + 2)(x + 2) = 284

Calculate the square root of the right side: 16.852299546

Break this problem into two subproblems by setting 
(x + 2) equal to 16.852299546 and -16.852299546.

Subproblem 1

x + 2 = 16.852299546 Simplifying x + 2 = 16.852299546 Reorder the terms: 2 + x = 16.852299546 Solving 2 + x = 16.852299546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 16.852299546 + -2 Combine like terms: 2 + -2 = 0 0 + x = 16.852299546 + -2 x = 16.852299546 + -2 Combine like terms: 16.852299546 + -2 = 14.852299546 x = 14.852299546 Simplifying x = 14.852299546

Subproblem 2

x + 2 = -16.852299546 Simplifying x + 2 = -16.852299546 Reorder the terms: 2 + x = -16.852299546 Solving 2 + x = -16.852299546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -16.852299546 + -2 Combine like terms: 2 + -2 = 0 0 + x = -16.852299546 + -2 x = -16.852299546 + -2 Combine like terms: -16.852299546 + -2 = -18.852299546 x = -18.852299546 Simplifying x = -18.852299546

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.852299546, -18.852299546}

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