x^2+x-300=0

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Solution for x^2+x-300=0 equation:


Simplifying
x2 + x + -300 = 0

Reorder the terms:
-300 + x + x2 = 0

Solving
-300 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + x + x2 = 0 + 300
x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
x + x2 = 300

The x term is x.  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.
x + 0.25 + x2 = 300 + 0.25

Reorder the terms:
0.25 + x + x2 = 300 + 0.25

Combine like terms: 300 + 0.25 = 300.25
0.25 + x + x2 = 300.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 300.25

Calculate the square root of the right side: 17.327723451

Break this problem into two subproblems by setting 
(x + 0.5) equal to 17.327723451 and -17.327723451.

Subproblem 1

x + 0.5 = 17.327723451 Simplifying x + 0.5 = 17.327723451 Reorder the terms: 0.5 + x = 17.327723451 Solving 0.5 + x = 17.327723451 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 = 17.327723451 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 17.327723451 + -0.5 x = 17.327723451 + -0.5 Combine like terms: 17.327723451 + -0.5 = 16.827723451 x = 16.827723451 Simplifying x = 16.827723451

Subproblem 2

x + 0.5 = -17.327723451 Simplifying x + 0.5 = -17.327723451 Reorder the terms: 0.5 + x = -17.327723451 Solving 0.5 + x = -17.327723451 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 = -17.327723451 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -17.327723451 + -0.5 x = -17.327723451 + -0.5 Combine like terms: -17.327723451 + -0.5 = -17.827723451 x = -17.827723451 Simplifying x = -17.827723451

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.827723451, -17.827723451}

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