x^2+30x+99=0

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Solution for x^2+30x+99=0 equation:


Simplifying
x2 + 30x + 99 = 0

Reorder the terms:
99 + 30x + x2 = 0

Solving
99 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-99' to each side of the equation.
99 + 30x + -99 + x2 = 0 + -99

Reorder the terms:
99 + -99 + 30x + x2 = 0 + -99

Combine like terms: 99 + -99 = 0
0 + 30x + x2 = 0 + -99
30x + x2 = 0 + -99

Combine like terms: 0 + -99 = -99
30x + x2 = -99

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 = -99 + 225

Reorder the terms:
225 + 30x + x2 = -99 + 225

Combine like terms: -99 + 225 = 126
225 + 30x + x2 = 126

Factor a perfect square on the left side:
(x + 15)(x + 15) = 126

Calculate the square root of the right side: 11.22497216

Break this problem into two subproblems by setting 
(x + 15) equal to 11.22497216 and -11.22497216.

Subproblem 1

x + 15 = 11.22497216 Simplifying x + 15 = 11.22497216 Reorder the terms: 15 + x = 11.22497216 Solving 15 + x = 11.22497216 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 = 11.22497216 + -15 Combine like terms: 15 + -15 = 0 0 + x = 11.22497216 + -15 x = 11.22497216 + -15 Combine like terms: 11.22497216 + -15 = -3.77502784 x = -3.77502784 Simplifying x = -3.77502784

Subproblem 2

x + 15 = -11.22497216 Simplifying x + 15 = -11.22497216 Reorder the terms: 15 + x = -11.22497216 Solving 15 + x = -11.22497216 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 = -11.22497216 + -15 Combine like terms: 15 + -15 = 0 0 + x = -11.22497216 + -15 x = -11.22497216 + -15 Combine like terms: -11.22497216 + -15 = -26.22497216 x = -26.22497216 Simplifying x = -26.22497216

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.77502784, -26.22497216}

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