x^2+27x+63=0

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Solution for x^2+27x+63=0 equation:


Simplifying
x2 + 27x + 63 = 0

Reorder the terms:
63 + 27x + x2 = 0

Solving
63 + 27x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-63' to each side of the equation.
63 + 27x + -63 + x2 = 0 + -63

Reorder the terms:
63 + -63 + 27x + x2 = 0 + -63

Combine like terms: 63 + -63 = 0
0 + 27x + x2 = 0 + -63
27x + x2 = 0 + -63

Combine like terms: 0 + -63 = -63
27x + x2 = -63

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 = -63 + 182.25

Reorder the terms:
182.25 + 27x + x2 = -63 + 182.25

Combine like terms: -63 + 182.25 = 119.25
182.25 + 27x + x2 = 119.25

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 119.25

Calculate the square root of the right side: 10.920164834

Break this problem into two subproblems by setting 
(x + 13.5) equal to 10.920164834 and -10.920164834.

Subproblem 1

x + 13.5 = 10.920164834 Simplifying x + 13.5 = 10.920164834 Reorder the terms: 13.5 + x = 10.920164834 Solving 13.5 + x = 10.920164834 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 = 10.920164834 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 10.920164834 + -13.5 x = 10.920164834 + -13.5 Combine like terms: 10.920164834 + -13.5 = -2.579835166 x = -2.579835166 Simplifying x = -2.579835166

Subproblem 2

x + 13.5 = -10.920164834 Simplifying x + 13.5 = -10.920164834 Reorder the terms: 13.5 + x = -10.920164834 Solving 13.5 + x = -10.920164834 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 = -10.920164834 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -10.920164834 + -13.5 x = -10.920164834 + -13.5 Combine like terms: -10.920164834 + -13.5 = -24.420164834 x = -24.420164834 Simplifying x = -24.420164834

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.579835166, -24.420164834}

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