X(X+4)=113

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Solution for X(X+4)=113 equation:


Simplifying
X(X + 4) = 113

Reorder the terms:
X(4 + X) = 113
(4 * X + X * X) = 113
(4X + X2) = 113

Solving
4X + X2 = 113

Solving for variable 'X'.

Reorder the terms:
-113 + 4X + X2 = 113 + -113

Combine like terms: 113 + -113 = 0
-113 + 4X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '113' to each side of the equation.
-113 + 4X + 113 + X2 = 0 + 113

Reorder the terms:
-113 + 113 + 4X + X2 = 0 + 113

Combine like terms: -113 + 113 = 0
0 + 4X + X2 = 0 + 113
4X + X2 = 0 + 113

Combine like terms: 0 + 113 = 113
4X + X2 = 113

The X term is 4X.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4X + 4 + X2 = 113 + 4

Reorder the terms:
4 + 4X + X2 = 113 + 4

Combine like terms: 113 + 4 = 117
4 + 4X + X2 = 117

Factor a perfect square on the left side:
(X + 2)(X + 2) = 117

Calculate the square root of the right side: 10.816653826

Break this problem into two subproblems by setting 
(X + 2) equal to 10.816653826 and -10.816653826.

Subproblem 1

X + 2 = 10.816653826 Simplifying X + 2 = 10.816653826 Reorder the terms: 2 + X = 10.816653826 Solving 2 + X = 10.816653826 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 10.816653826 + -2 Combine like terms: 2 + -2 = 0 0 + X = 10.816653826 + -2 X = 10.816653826 + -2 Combine like terms: 10.816653826 + -2 = 8.816653826 X = 8.816653826 Simplifying X = 8.816653826

Subproblem 2

X + 2 = -10.816653826 Simplifying X + 2 = -10.816653826 Reorder the terms: 2 + X = -10.816653826 Solving 2 + X = -10.816653826 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = -10.816653826 + -2 Combine like terms: 2 + -2 = 0 0 + X = -10.816653826 + -2 X = -10.816653826 + -2 Combine like terms: -10.816653826 + -2 = -12.816653826 X = -12.816653826 Simplifying X = -12.816653826

Solution

The solution to the problem is based on the solutions from the subproblems. X = {8.816653826, -12.816653826}

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