x(30-x)=100

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Solution for x(30-x)=100 equation:


Simplifying
x(30 + -1x) = 100
(30 * x + -1x * x) = 100
(30x + -1x2) = 100

Solving
30x + -1x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 30x + -1x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 30x + -1x2 = 0

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

Divide each side by '-1'.
100 + -30x + x2 = 0

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -30x + -100 + x2 = 0 + -100

Reorder the terms:
100 + -100 + -30x + x2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -30x + x2 = 0 + -100
-30x + x2 = 0 + -100

Combine like terms: 0 + -100 = -100
-30x + x2 = -100

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 = -100 + 225

Reorder the terms:
225 + -30x + x2 = -100 + 225

Combine like terms: -100 + 225 = 125
225 + -30x + x2 = 125

Factor a perfect square on the left side:
(x + -15)(x + -15) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(x + -15) equal to 11.180339887 and -11.180339887.

Subproblem 1

x + -15 = 11.180339887 Simplifying x + -15 = 11.180339887 Reorder the terms: -15 + x = 11.180339887 Solving -15 + x = 11.180339887 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 = 11.180339887 + 15 Combine like terms: -15 + 15 = 0 0 + x = 11.180339887 + 15 x = 11.180339887 + 15 Combine like terms: 11.180339887 + 15 = 26.180339887 x = 26.180339887 Simplifying x = 26.180339887

Subproblem 2

x + -15 = -11.180339887 Simplifying x + -15 = -11.180339887 Reorder the terms: -15 + x = -11.180339887 Solving -15 + x = -11.180339887 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 = -11.180339887 + 15 Combine like terms: -15 + 15 = 0 0 + x = -11.180339887 + 15 x = -11.180339887 + 15 Combine like terms: -11.180339887 + 15 = 3.819660113 x = 3.819660113 Simplifying x = 3.819660113

Solution

The solution to the problem is based on the solutions from the subproblems. x = {26.180339887, 3.819660113}

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