x^2-3x-256=0

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Solution for x^2-3x-256=0 equation:


Simplifying
x2 + -3x + -256 = 0

Reorder the terms:
-256 + -3x + x2 = 0

Solving
-256 + -3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '256' to each side of the equation.
-256 + -3x + 256 + x2 = 0 + 256

Reorder the terms:
-256 + 256 + -3x + x2 = 0 + 256

Combine like terms: -256 + 256 = 0
0 + -3x + x2 = 0 + 256
-3x + x2 = 0 + 256

Combine like terms: 0 + 256 = 256
-3x + x2 = 256

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 = 256 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 256 + 2.25

Combine like terms: 256 + 2.25 = 258.25
2.25 + -3x + x2 = 258.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 258.25

Calculate the square root of the right side: 16.07015868

Break this problem into two subproblems by setting 
(x + -1.5) equal to 16.07015868 and -16.07015868.

Subproblem 1

x + -1.5 = 16.07015868 Simplifying x + -1.5 = 16.07015868 Reorder the terms: -1.5 + x = 16.07015868 Solving -1.5 + x = 16.07015868 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 = 16.07015868 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 16.07015868 + 1.5 x = 16.07015868 + 1.5 Combine like terms: 16.07015868 + 1.5 = 17.57015868 x = 17.57015868 Simplifying x = 17.57015868

Subproblem 2

x + -1.5 = -16.07015868 Simplifying x + -1.5 = -16.07015868 Reorder the terms: -1.5 + x = -16.07015868 Solving -1.5 + x = -16.07015868 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 = -16.07015868 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -16.07015868 + 1.5 x = -16.07015868 + 1.5 Combine like terms: -16.07015868 + 1.5 = -14.57015868 x = -14.57015868 Simplifying x = -14.57015868

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.57015868, -14.57015868}

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