(30-x)*x=36

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Solution for (30-x)*x=36 equation:


Simplifying
(30 + -1x) * x = 36

Reorder the terms for easier multiplication:
x(30 + -1x) = 36
(30 * x + -1x * x) = 36
(30x + -1x2) = 36

Solving
30x + -1x2 = 36

Solving for variable 'x'.

Reorder the terms:
-36 + 30x + -1x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 30x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
36 + -30x + x2 = 0

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -30x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + -30x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -30x + x2 = 0 + -36
-30x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
-30x + x2 = -36

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 = -36 + 225

Reorder the terms:
225 + -30x + x2 = -36 + 225

Combine like terms: -36 + 225 = 189
225 + -30x + x2 = 189

Factor a perfect square on the left side:
(x + -15)(x + -15) = 189

Calculate the square root of the right side: 13.747727085

Break this problem into two subproblems by setting 
(x + -15) equal to 13.747727085 and -13.747727085.

Subproblem 1

x + -15 = 13.747727085 Simplifying x + -15 = 13.747727085 Reorder the terms: -15 + x = 13.747727085 Solving -15 + x = 13.747727085 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 = 13.747727085 + 15 Combine like terms: -15 + 15 = 0 0 + x = 13.747727085 + 15 x = 13.747727085 + 15 Combine like terms: 13.747727085 + 15 = 28.747727085 x = 28.747727085 Simplifying x = 28.747727085

Subproblem 2

x + -15 = -13.747727085 Simplifying x + -15 = -13.747727085 Reorder the terms: -15 + x = -13.747727085 Solving -15 + x = -13.747727085 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 = -13.747727085 + 15 Combine like terms: -15 + 15 = 0 0 + x = -13.747727085 + 15 x = -13.747727085 + 15 Combine like terms: -13.747727085 + 15 = 1.252272915 x = 1.252272915 Simplifying x = 1.252272915

Solution

The solution to the problem is based on the solutions from the subproblems. x = {28.747727085, 1.252272915}

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