(x+30)x=5000

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Solution for (x+30)x=5000 equation:


Simplifying
(x + 30) * x = 5000

Reorder the terms:
(30 + x) * x = 5000

Reorder the terms for easier multiplication:
x(30 + x) = 5000
(30 * x + x * x) = 5000
(30x + x2) = 5000

Solving
30x + x2 = 5000

Solving for variable 'x'.

Reorder the terms:
-5000 + 30x + x2 = 5000 + -5000

Combine like terms: 5000 + -5000 = 0
-5000 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5000' to each side of the equation.
-5000 + 30x + 5000 + x2 = 0 + 5000

Reorder the terms:
-5000 + 5000 + 30x + x2 = 0 + 5000

Combine like terms: -5000 + 5000 = 0
0 + 30x + x2 = 0 + 5000
30x + x2 = 0 + 5000

Combine like terms: 0 + 5000 = 5000
30x + x2 = 5000

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = 5000 + 225

Reorder the terms:
225 + 30x + x2 = 5000 + 225

Combine like terms: 5000 + 225 = 5225
225 + 30x + x2 = 5225

Factor a perfect square on the left side:
(x + 15)(x + 15) = 5225

Calculate the square root of the right side: 72.284161474

Break this problem into two subproblems by setting 
(x + 15) equal to 72.284161474 and -72.284161474.

Subproblem 1

x + 15 = 72.284161474 Simplifying x + 15 = 72.284161474 Reorder the terms: 15 + x = 72.284161474 Solving 15 + x = 72.284161474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 72.284161474 + -15 Combine like terms: 15 + -15 = 0 0 + x = 72.284161474 + -15 x = 72.284161474 + -15 Combine like terms: 72.284161474 + -15 = 57.284161474 x = 57.284161474 Simplifying x = 57.284161474

Subproblem 2

x + 15 = -72.284161474 Simplifying x + 15 = -72.284161474 Reorder the terms: 15 + x = -72.284161474 Solving 15 + x = -72.284161474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -72.284161474 + -15 Combine like terms: 15 + -15 = 0 0 + x = -72.284161474 + -15 x = -72.284161474 + -15 Combine like terms: -72.284161474 + -15 = -87.284161474 x = -87.284161474 Simplifying x = -87.284161474

Solution

The solution to the problem is based on the solutions from the subproblems. x = {57.284161474, -87.284161474}

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