x^2+3x-280=0

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Solution for x^2+3x-280=0 equation: 


Simplifying
x2 + 3x + -280 = 0

Reorder the terms:
-280 + 3x + x2 = 0

Solving
-280 + 3x + 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 + 3x + 280 + x2 = 0 + 280

Reorder the terms:
-280 + 280 + 3x + x2 = 0 + 280

Combine like terms: -280 + 280 = 0
0 + 3x + x2 = 0 + 280
3x + x2 = 0 + 280

Combine like terms: 0 + 280 = 280
3x + x2 = 280

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 280 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 280 + 2.25

Combine like terms: 280 + 2.25 = 282.25
2.25 + 3x + x2 = 282.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 282.25

Calculate the square root of the right side: 16.800297616

Break this problem into two subproblems by setting 
(x + 1.5) equal to 16.800297616 and -16.800297616.


Subproblem 1
x + 1.5 = 16.800297616

Simplifying
x + 1.5 = 16.800297616

Reorder the terms:
1.5 + x = 16.800297616

Solving
1.5 + x = 16.800297616

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 16.800297616 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 16.800297616 + -1.5
x = 16.800297616 + -1.5

Combine like terms: 16.800297616 + -1.5 = 15.300297616
x = 15.300297616

Simplifying
x = 15.300297616


Subproblem 2
x + 1.5 = -16.800297616

Simplifying
x + 1.5 = -16.800297616

Reorder the terms:
1.5 + x = -16.800297616

Solving
1.5 + x = -16.800297616

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -16.800297616 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -16.800297616 + -1.5
x = -16.800297616 + -1.5

Combine like terms: -16.800297616 + -1.5 = -18.300297616
x = -18.300297616

Simplifying
x = -18.300297616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.300297616, -18.300297616}

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