x^2-30x+60=

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Solution for x^2-30x+60= equation:


Simplifying
x2 + -30x + 60 = 0

Reorder the terms:
60 + -30x + x2 = 0

Solving
60 + -30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + -30x + -60 + x2 = 0 + -60

Reorder the terms:
60 + -60 + -30x + x2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -30x + x2 = 0 + -60
-30x + x2 = 0 + -60

Combine like terms: 0 + -60 = -60
-30x + x2 = -60

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 = -60 + 225

Reorder the terms:
225 + -30x + x2 = -60 + 225

Combine like terms: -60 + 225 = 165
225 + -30x + x2 = 165

Factor a perfect square on the left side:
(x + -15)(x + -15) = 165

Calculate the square root of the right side: 12.845232579

Break this problem into two subproblems by setting 
(x + -15) equal to 12.845232579 and -12.845232579.

Subproblem 1

x + -15 = 12.845232579 Simplifying x + -15 = 12.845232579 Reorder the terms: -15 + x = 12.845232579 Solving -15 + x = 12.845232579 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 = 12.845232579 + 15 Combine like terms: -15 + 15 = 0 0 + x = 12.845232579 + 15 x = 12.845232579 + 15 Combine like terms: 12.845232579 + 15 = 27.845232579 x = 27.845232579 Simplifying x = 27.845232579

Subproblem 2

x + -15 = -12.845232579 Simplifying x + -15 = -12.845232579 Reorder the terms: -15 + x = -12.845232579 Solving -15 + x = -12.845232579 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 = -12.845232579 + 15 Combine like terms: -15 + 15 = 0 0 + x = -12.845232579 + 15 x = -12.845232579 + 15 Combine like terms: -12.845232579 + 15 = 2.154767421 x = 2.154767421 Simplifying x = 2.154767421

Solution

The solution to the problem is based on the solutions from the subproblems. x = {27.845232579, 2.154767421}

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