x^2+23x-280=0

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Solution for x^2+23x-280=0 equation:


Simplifying
x2 + 23x + -280 = 0

Reorder the terms:
-280 + 23x + x2 = 0

Solving
-280 + 23x + 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 + 23x + 280 + x2 = 0 + 280

Reorder the terms:
-280 + 280 + 23x + x2 = 0 + 280

Combine like terms: -280 + 280 = 0
0 + 23x + x2 = 0 + 280
23x + x2 = 0 + 280

Combine like terms: 0 + 280 = 280
23x + x2 = 280

The x term is 23x.  Take half its coefficient (11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
23x + 132.25 + x2 = 280 + 132.25

Reorder the terms:
132.25 + 23x + x2 = 280 + 132.25

Combine like terms: 280 + 132.25 = 412.25
132.25 + 23x + x2 = 412.25

Factor a perfect square on the left side:
(x + 11.5)(x + 11.5) = 412.25

Calculate the square root of the right side: 20.303940504

Break this problem into two subproblems by setting 
(x + 11.5) equal to 20.303940504 and -20.303940504.

Subproblem 1

x + 11.5 = 20.303940504 Simplifying x + 11.5 = 20.303940504 Reorder the terms: 11.5 + x = 20.303940504 Solving 11.5 + x = 20.303940504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 20.303940504 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 20.303940504 + -11.5 x = 20.303940504 + -11.5 Combine like terms: 20.303940504 + -11.5 = 8.803940504 x = 8.803940504 Simplifying x = 8.803940504

Subproblem 2

x + 11.5 = -20.303940504 Simplifying x + 11.5 = -20.303940504 Reorder the terms: 11.5 + x = -20.303940504 Solving 11.5 + x = -20.303940504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -20.303940504 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -20.303940504 + -11.5 x = -20.303940504 + -11.5 Combine like terms: -20.303940504 + -11.5 = -31.803940504 x = -31.803940504 Simplifying x = -31.803940504

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.803940504, -31.803940504}

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