(X^2)+2X=144

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Solution for (X^2)+2X=144 equation:


Simplifying
(X2) + 2X = 144
X2 + 2X = 144

Reorder the terms:
2X + X2 = 144

Solving
2X + X2 = 144

Solving for variable 'X'.

Reorder the terms:
-144 + 2X + X2 = 144 + -144

Combine like terms: 144 + -144 = 0
-144 + 2X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + 2X + 144 + X2 = 0 + 144

Reorder the terms:
-144 + 144 + 2X + X2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + 2X + X2 = 0 + 144
2X + X2 = 0 + 144

Combine like terms: 0 + 144 = 144
2X + X2 = 144

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 = 144 + 1

Reorder the terms:
1 + 2X + X2 = 144 + 1

Combine like terms: 144 + 1 = 145
1 + 2X + X2 = 145

Factor a perfect square on the left side:
(X + 1)(X + 1) = 145

Calculate the square root of the right side: 12.041594579

Break this problem into two subproblems by setting 
(X + 1) equal to 12.041594579 and -12.041594579.

Subproblem 1

X + 1 = 12.041594579 Simplifying X + 1 = 12.041594579 Reorder the terms: 1 + X = 12.041594579 Solving 1 + X = 12.041594579 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 = 12.041594579 + -1 Combine like terms: 1 + -1 = 0 0 + X = 12.041594579 + -1 X = 12.041594579 + -1 Combine like terms: 12.041594579 + -1 = 11.041594579 X = 11.041594579 Simplifying X = 11.041594579

Subproblem 2

X + 1 = -12.041594579 Simplifying X + 1 = -12.041594579 Reorder the terms: 1 + X = -12.041594579 Solving 1 + X = -12.041594579 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 = -12.041594579 + -1 Combine like terms: 1 + -1 = 0 0 + X = -12.041594579 + -1 X = -12.041594579 + -1 Combine like terms: -12.041594579 + -1 = -13.041594579 X = -13.041594579 Simplifying X = -13.041594579

Solution

The solution to the problem is based on the solutions from the subproblems. X = {11.041594579, -13.041594579}

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