X^2+2X=300

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Solution for X^2+2X=300 equation:


Simplifying
X2 + 2X = 300

Reorder the terms:
2X + X2 = 300

Solving
2X + X2 = 300

Solving for variable 'X'.

Reorder the terms:
-300 + 2X + X2 = 300 + -300

Combine like terms: 300 + -300 = 0
-300 + 2X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + 2X + 300 + X2 = 0 + 300

Reorder the terms:
-300 + 300 + 2X + X2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + 2X + X2 = 0 + 300
2X + X2 = 0 + 300

Combine like terms: 0 + 300 = 300
2X + X2 = 300

The X term is 2X.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2X + 1 + X2 = 300 + 1

Reorder the terms:
1 + 2X + X2 = 300 + 1

Combine like terms: 300 + 1 = 301
1 + 2X + X2 = 301

Factor a perfect square on the left side:
(X + 1)(X + 1) = 301

Calculate the square root of the right side: 17.349351573

Break this problem into two subproblems by setting 
(X + 1) equal to 17.349351573 and -17.349351573.

Subproblem 1

X + 1 = 17.349351573 Simplifying X + 1 = 17.349351573 Reorder the terms: 1 + X = 17.349351573 Solving 1 + X = 17.349351573 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = 17.349351573 + -1 Combine like terms: 1 + -1 = 0 0 + X = 17.349351573 + -1 X = 17.349351573 + -1 Combine like terms: 17.349351573 + -1 = 16.349351573 X = 16.349351573 Simplifying X = 16.349351573

Subproblem 2

X + 1 = -17.349351573 Simplifying X + 1 = -17.349351573 Reorder the terms: 1 + X = -17.349351573 Solving 1 + X = -17.349351573 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = -17.349351573 + -1 Combine like terms: 1 + -1 = 0 0 + X = -17.349351573 + -1 X = -17.349351573 + -1 Combine like terms: -17.349351573 + -1 = -18.349351573 X = -18.349351573 Simplifying X = -18.349351573

Solution

The solution to the problem is based on the solutions from the subproblems. X = {16.349351573, -18.349351573}

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