x(x+4)=400

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Solution for x(x+4)=400 equation:


Simplifying
x(x + 4) = 400

Reorder the terms:
x(4 + x) = 400
(4 * x + x * x) = 400
(4x + x2) = 400

Solving
4x + x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + 4x + x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + 4x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + 4x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + 4x + x2 = 0 + 400
4x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
4x + x2 = 400

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 = 400 + 4

Reorder the terms:
4 + 4x + x2 = 400 + 4

Combine like terms: 400 + 4 = 404
4 + 4x + x2 = 404

Factor a perfect square on the left side:
(x + 2)(x + 2) = 404

Calculate the square root of the right side: 20.099751242

Break this problem into two subproblems by setting 
(x + 2) equal to 20.099751242 and -20.099751242.

Subproblem 1

x + 2 = 20.099751242 Simplifying x + 2 = 20.099751242 Reorder the terms: 2 + x = 20.099751242 Solving 2 + x = 20.099751242 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 = 20.099751242 + -2 Combine like terms: 2 + -2 = 0 0 + x = 20.099751242 + -2 x = 20.099751242 + -2 Combine like terms: 20.099751242 + -2 = 18.099751242 x = 18.099751242 Simplifying x = 18.099751242

Subproblem 2

x + 2 = -20.099751242 Simplifying x + 2 = -20.099751242 Reorder the terms: 2 + x = -20.099751242 Solving 2 + x = -20.099751242 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 = -20.099751242 + -2 Combine like terms: 2 + -2 = 0 0 + x = -20.099751242 + -2 x = -20.099751242 + -2 Combine like terms: -20.099751242 + -2 = -22.099751242 x = -22.099751242 Simplifying x = -22.099751242

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.099751242, -22.099751242}

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