x^2+3x+27=180

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Solution for x^2+3x+27=180 equation:


Simplifying
x2 + 3x + 27 = 180

Reorder the terms:
27 + 3x + x2 = 180

Solving
27 + 3x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
27 + -180 + 3x + x2 = 180 + -180

Combine like terms: 27 + -180 = -153
-153 + 3x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-153 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '153' to each side of the equation.
-153 + 3x + 153 + x2 = 0 + 153

Reorder the terms:
-153 + 153 + 3x + x2 = 0 + 153

Combine like terms: -153 + 153 = 0
0 + 3x + x2 = 0 + 153
3x + x2 = 0 + 153

Combine like terms: 0 + 153 = 153
3x + x2 = 153

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 153 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 153 + 2.25

Combine like terms: 153 + 2.25 = 155.25
2.25 + 3x + x2 = 155.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 155.25

Calculate the square root of the right side: 12.459935794

Break this problem into two subproblems by setting 
(x + 1.5) equal to 12.459935794 and -12.459935794.

Subproblem 1

x + 1.5 = 12.459935794 Simplifying x + 1.5 = 12.459935794 Reorder the terms: 1.5 + x = 12.459935794 Solving 1.5 + x = 12.459935794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 12.459935794 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.459935794 + -1.5 x = 12.459935794 + -1.5 Combine like terms: 12.459935794 + -1.5 = 10.959935794 x = 10.959935794 Simplifying x = 10.959935794

Subproblem 2

x + 1.5 = -12.459935794 Simplifying x + 1.5 = -12.459935794 Reorder the terms: 1.5 + x = -12.459935794 Solving 1.5 + x = -12.459935794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -12.459935794 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.459935794 + -1.5 x = -12.459935794 + -1.5 Combine like terms: -12.459935794 + -1.5 = -13.959935794 x = -13.959935794 Simplifying x = -13.959935794

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.959935794, -13.959935794}

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