2X(X+4)=25

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Solution for 2X(X+4)=25 equation:


Simplifying
2X(X + 4) = 25

Reorder the terms:
2X(4 + X) = 25
(4 * 2X + X * 2X) = 25
(8X + 2X2) = 25

Solving
8X + 2X2 = 25

Solving for variable 'X'.

Reorder the terms:
-25 + 8X + 2X2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 8X + 2X2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-12.5 + 4X + X2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + 4X + 12.5 + X2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + 4X + X2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + 4X + X2 = 0 + 12.5
4X + X2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
4X + X2 = 12.5

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 = 12.5 + 4

Reorder the terms:
4 + 4X + X2 = 12.5 + 4

Combine like terms: 12.5 + 4 = 16.5
4 + 4X + X2 = 16.5

Factor a perfect square on the left side:
(X + 2)(X + 2) = 16.5

Calculate the square root of the right side: 4.062019202

Break this problem into two subproblems by setting 
(X + 2) equal to 4.062019202 and -4.062019202.

Subproblem 1

X + 2 = 4.062019202 Simplifying X + 2 = 4.062019202 Reorder the terms: 2 + X = 4.062019202 Solving 2 + X = 4.062019202 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 = 4.062019202 + -2 Combine like terms: 2 + -2 = 0 0 + X = 4.062019202 + -2 X = 4.062019202 + -2 Combine like terms: 4.062019202 + -2 = 2.062019202 X = 2.062019202 Simplifying X = 2.062019202

Subproblem 2

X + 2 = -4.062019202 Simplifying X + 2 = -4.062019202 Reorder the terms: 2 + X = -4.062019202 Solving 2 + X = -4.062019202 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 = -4.062019202 + -2 Combine like terms: 2 + -2 = 0 0 + X = -4.062019202 + -2 X = -4.062019202 + -2 Combine like terms: -4.062019202 + -2 = -6.062019202 X = -6.062019202 Simplifying X = -6.062019202

Solution

The solution to the problem is based on the solutions from the subproblems. X = {2.062019202, -6.062019202}

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