x^2+27x+177=0

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Solution for x^2+27x+177=0 equation:


Simplifying
x2 + 27x + 177 = 0

Reorder the terms:
177 + 27x + x2 = 0

Solving
177 + 27x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-177' to each side of the equation.
177 + 27x + -177 + x2 = 0 + -177

Reorder the terms:
177 + -177 + 27x + x2 = 0 + -177

Combine like terms: 177 + -177 = 0
0 + 27x + x2 = 0 + -177
27x + x2 = 0 + -177

Combine like terms: 0 + -177 = -177
27x + x2 = -177

The x term is 27x.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27x + 182.25 + x2 = -177 + 182.25

Reorder the terms:
182.25 + 27x + x2 = -177 + 182.25

Combine like terms: -177 + 182.25 = 5.25
182.25 + 27x + x2 = 5.25

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 13.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

x + 13.5 = 2.291287847 Simplifying x + 13.5 = 2.291287847 Reorder the terms: 13.5 + x = 2.291287847 Solving 13.5 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 2.291287847 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 2.291287847 + -13.5 x = 2.291287847 + -13.5 Combine like terms: 2.291287847 + -13.5 = -11.208712153 x = -11.208712153 Simplifying x = -11.208712153

Subproblem 2

x + 13.5 = -2.291287847 Simplifying x + 13.5 = -2.291287847 Reorder the terms: 13.5 + x = -2.291287847 Solving 13.5 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -2.291287847 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -2.291287847 + -13.5 x = -2.291287847 + -13.5 Combine like terms: -2.291287847 + -13.5 = -15.791287847 x = -15.791287847 Simplifying x = -15.791287847

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-11.208712153, -15.791287847}

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