x^2+17x+27=0

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Solution for x^2+17x+27=0 equation:


Simplifying
x2 + 17x + 27 = 0

Reorder the terms:
27 + 17x + x2 = 0

Solving
27 + 17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + 17x + -27 + x2 = 0 + -27

Reorder the terms:
27 + -27 + 17x + x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 17x + x2 = 0 + -27
17x + x2 = 0 + -27

Combine like terms: 0 + -27 = -27
17x + x2 = -27

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = -27 + 72.25

Reorder the terms:
72.25 + 17x + x2 = -27 + 72.25

Combine like terms: -27 + 72.25 = 45.25
72.25 + 17x + x2 = 45.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 45.25

Calculate the square root of the right side: 6.726812024

Break this problem into two subproblems by setting 
(x + 8.5) equal to 6.726812024 and -6.726812024.

Subproblem 1

x + 8.5 = 6.726812024 Simplifying x + 8.5 = 6.726812024 Reorder the terms: 8.5 + x = 6.726812024 Solving 8.5 + x = 6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 6.726812024 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 6.726812024 + -8.5 x = 6.726812024 + -8.5 Combine like terms: 6.726812024 + -8.5 = -1.773187976 x = -1.773187976 Simplifying x = -1.773187976

Subproblem 2

x + 8.5 = -6.726812024 Simplifying x + 8.5 = -6.726812024 Reorder the terms: 8.5 + x = -6.726812024 Solving 8.5 + x = -6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -6.726812024 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -6.726812024 + -8.5 x = -6.726812024 + -8.5 Combine like terms: -6.726812024 + -8.5 = -15.226812024 x = -15.226812024 Simplifying x = -15.226812024

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.773187976, -15.226812024}

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