x^2-30x+75=0

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Solution for x^2-30x+75=0 equation:


Simplifying
x2 + -30x + 75 = 0

Reorder the terms:
75 + -30x + x2 = 0

Solving
75 + -30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-75' to each side of the equation.
75 + -30x + -75 + x2 = 0 + -75

Reorder the terms:
75 + -75 + -30x + x2 = 0 + -75

Combine like terms: 75 + -75 = 0
0 + -30x + x2 = 0 + -75
-30x + x2 = 0 + -75

Combine like terms: 0 + -75 = -75
-30x + x2 = -75

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 = -75 + 225

Reorder the terms:
225 + -30x + x2 = -75 + 225

Combine like terms: -75 + 225 = 150
225 + -30x + x2 = 150

Factor a perfect square on the left side:
(x + -15)(x + -15) = 150

Calculate the square root of the right side: 12.247448714

Break this problem into two subproblems by setting 
(x + -15) equal to 12.247448714 and -12.247448714.

Subproblem 1

x + -15 = 12.247448714 Simplifying x + -15 = 12.247448714 Reorder the terms: -15 + x = 12.247448714 Solving -15 + x = 12.247448714 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 = 12.247448714 + 15 Combine like terms: -15 + 15 = 0 0 + x = 12.247448714 + 15 x = 12.247448714 + 15 Combine like terms: 12.247448714 + 15 = 27.247448714 x = 27.247448714 Simplifying x = 27.247448714

Subproblem 2

x + -15 = -12.247448714 Simplifying x + -15 = -12.247448714 Reorder the terms: -15 + x = -12.247448714 Solving -15 + x = -12.247448714 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 = -12.247448714 + 15 Combine like terms: -15 + 15 = 0 0 + x = -12.247448714 + 15 x = -12.247448714 + 15 Combine like terms: -12.247448714 + 15 = 2.752551286 x = 2.752551286 Simplifying x = 2.752551286

Solution

The solution to the problem is based on the solutions from the subproblems. x = {27.247448714, 2.752551286}

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