x^2+30x+54=0

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Solution for x^2+30x+54=0 equation:


Simplifying
x2 + 30x + 54 = 0

Reorder the terms:
54 + 30x + x2 = 0

Solving
54 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-54' to each side of the equation.
54 + 30x + -54 + x2 = 0 + -54

Reorder the terms:
54 + -54 + 30x + x2 = 0 + -54

Combine like terms: 54 + -54 = 0
0 + 30x + x2 = 0 + -54
30x + x2 = 0 + -54

Combine like terms: 0 + -54 = -54
30x + x2 = -54

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 = -54 + 225

Reorder the terms:
225 + 30x + x2 = -54 + 225

Combine like terms: -54 + 225 = 171
225 + 30x + x2 = 171

Factor a perfect square on the left side:
(x + 15)(x + 15) = 171

Calculate the square root of the right side: 13.076696831

Break this problem into two subproblems by setting 
(x + 15) equal to 13.076696831 and -13.076696831.

Subproblem 1

x + 15 = 13.076696831 Simplifying x + 15 = 13.076696831 Reorder the terms: 15 + x = 13.076696831 Solving 15 + x = 13.076696831 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 = 13.076696831 + -15 Combine like terms: 15 + -15 = 0 0 + x = 13.076696831 + -15 x = 13.076696831 + -15 Combine like terms: 13.076696831 + -15 = -1.923303169 x = -1.923303169 Simplifying x = -1.923303169

Subproblem 2

x + 15 = -13.076696831 Simplifying x + 15 = -13.076696831 Reorder the terms: 15 + x = -13.076696831 Solving 15 + x = -13.076696831 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 = -13.076696831 + -15 Combine like terms: 15 + -15 = 0 0 + x = -13.076696831 + -15 x = -13.076696831 + -15 Combine like terms: -13.076696831 + -15 = -28.076696831 x = -28.076696831 Simplifying x = -28.076696831

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.923303169, -28.076696831}

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