(3+x)x=400

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Solution for (3+x)x=400 equation:


Simplifying
(3 + x) * x = 400

Reorder the terms for easier multiplication:
x(3 + x) = 400
(3 * x + x * x) = 400
(3x + x2) = 400

Solving
3x + x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + 3x + x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + 3x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + 3x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + 3x + x2 = 0 + 400
3x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
3x + x2 = 400

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 400 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 400 + 2.25

Combine like terms: 400 + 2.25 = 402.25
2.25 + 3x + x2 = 402.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 402.25

Calculate the square root of the right side: 20.05617112

Break this problem into two subproblems by setting 
(x + 1.5) equal to 20.05617112 and -20.05617112.

Subproblem 1

x + 1.5 = 20.05617112 Simplifying x + 1.5 = 20.05617112 Reorder the terms: 1.5 + x = 20.05617112 Solving 1.5 + x = 20.05617112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 20.05617112 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 20.05617112 + -1.5 x = 20.05617112 + -1.5 Combine like terms: 20.05617112 + -1.5 = 18.55617112 x = 18.55617112 Simplifying x = 18.55617112

Subproblem 2

x + 1.5 = -20.05617112 Simplifying x + 1.5 = -20.05617112 Reorder the terms: 1.5 + x = -20.05617112 Solving 1.5 + x = -20.05617112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -20.05617112 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -20.05617112 + -1.5 x = -20.05617112 + -1.5 Combine like terms: -20.05617112 + -1.5 = -21.55617112 x = -21.55617112 Simplifying x = -21.55617112

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.55617112, -21.55617112}

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