x^2-x-303=0

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Solution for x^2-x-303=0 equation:


Simplifying
x2 + -1x + -303 = 0

Reorder the terms:
-303 + -1x + x2 = 0

Solving
-303 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '303' to each side of the equation.
-303 + -1x + 303 + x2 = 0 + 303

Reorder the terms:
-303 + 303 + -1x + x2 = 0 + 303

Combine like terms: -303 + 303 = 0
0 + -1x + x2 = 0 + 303
-1x + x2 = 0 + 303

Combine like terms: 0 + 303 = 303
-1x + x2 = 303

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 303 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 303 + 0.25

Combine like terms: 303 + 0.25 = 303.25
0.25 + -1x + x2 = 303.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 303.25

Calculate the square root of the right side: 17.414074767

Break this problem into two subproblems by setting 
(x + -0.5) equal to 17.414074767 and -17.414074767.

Subproblem 1

x + -0.5 = 17.414074767 Simplifying x + -0.5 = 17.414074767 Reorder the terms: -0.5 + x = 17.414074767 Solving -0.5 + x = 17.414074767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 17.414074767 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 17.414074767 + 0.5 x = 17.414074767 + 0.5 Combine like terms: 17.414074767 + 0.5 = 17.914074767 x = 17.914074767 Simplifying x = 17.914074767

Subproblem 2

x + -0.5 = -17.414074767 Simplifying x + -0.5 = -17.414074767 Reorder the terms: -0.5 + x = -17.414074767 Solving -0.5 + x = -17.414074767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -17.414074767 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -17.414074767 + 0.5 x = -17.414074767 + 0.5 Combine like terms: -17.414074767 + 0.5 = -16.914074767 x = -16.914074767 Simplifying x = -16.914074767

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.914074767, -16.914074767}

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