30x-x^2=30

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Solution for 30x-x^2=30 equation:


Simplifying
30x + -1x2 = 30

Solving
30x + -1x2 = 30

Solving for variable 'x'.

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

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

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

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

Move the constant term to the right:

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

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

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

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

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 = -30 + 225

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

Combine like terms: -30 + 225 = 195
225 + -30x + x2 = 195

Factor a perfect square on the left side:
(x + -15)(x + -15) = 195

Calculate the square root of the right side: 13.964240044

Break this problem into two subproblems by setting 
(x + -15) equal to 13.964240044 and -13.964240044.

Subproblem 1

x + -15 = 13.964240044 Simplifying x + -15 = 13.964240044 Reorder the terms: -15 + x = 13.964240044 Solving -15 + x = 13.964240044 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 = 13.964240044 + 15 Combine like terms: -15 + 15 = 0 0 + x = 13.964240044 + 15 x = 13.964240044 + 15 Combine like terms: 13.964240044 + 15 = 28.964240044 x = 28.964240044 Simplifying x = 28.964240044

Subproblem 2

x + -15 = -13.964240044 Simplifying x + -15 = -13.964240044 Reorder the terms: -15 + x = -13.964240044 Solving -15 + x = -13.964240044 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 = -13.964240044 + 15 Combine like terms: -15 + 15 = 0 0 + x = -13.964240044 + 15 x = -13.964240044 + 15 Combine like terms: -13.964240044 + 15 = 1.035759956 x = 1.035759956 Simplifying x = 1.035759956

Solution

The solution to the problem is based on the solutions from the subproblems. x = {28.964240044, 1.035759956}

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