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 = -2.154767421 x = -2.154767421 Simplifying x = -2.154767421

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 = -27.845232579 x = -27.845232579 Simplifying x = -27.845232579

Solution

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

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