x^2-30x+8.2=0

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Solution for x^2-30x+8.2=0 equation:


Simplifying
x2 + -30x + 8.2 = 0

Reorder the terms:
8.2 + -30x + x2 = 0

Solving
8.2 + -30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-8.2' to each side of the equation.
8.2 + -30x + -8.2 + x2 = 0 + -8.2

Reorder the terms:
8.2 + -8.2 + -30x + x2 = 0 + -8.2

Combine like terms: 8.2 + -8.2 = 0.0
0.0 + -30x + x2 = 0 + -8.2
-30x + x2 = 0 + -8.2

Combine like terms: 0 + -8.2 = -8.2
-30x + x2 = -8.2

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 = -8.2 + 225

Reorder the terms:
225 + -30x + x2 = -8.2 + 225

Combine like terms: -8.2 + 225 = 216.8
225 + -30x + x2 = 216.8

Factor a perfect square on the left side:
(x + -15)(x + -15) = 216.8

Calculate the square root of the right side: 14.724129855

Break this problem into two subproblems by setting 
(x + -15) equal to 14.724129855 and -14.724129855.

Subproblem 1

x + -15 = 14.724129855 Simplifying x + -15 = 14.724129855 Reorder the terms: -15 + x = 14.724129855 Solving -15 + x = 14.724129855 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 = 14.724129855 + 15 Combine like terms: -15 + 15 = 0 0 + x = 14.724129855 + 15 x = 14.724129855 + 15 Combine like terms: 14.724129855 + 15 = 29.724129855 x = 29.724129855 Simplifying x = 29.724129855

Subproblem 2

x + -15 = -14.724129855 Simplifying x + -15 = -14.724129855 Reorder the terms: -15 + x = -14.724129855 Solving -15 + x = -14.724129855 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 = -14.724129855 + 15 Combine like terms: -15 + 15 = 0 0 + x = -14.724129855 + 15 x = -14.724129855 + 15 Combine like terms: -14.724129855 + 15 = 0.275870145 x = 0.275870145 Simplifying x = 0.275870145

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.724129855, 0.275870145}

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