x^2+17x+56=0

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Solution for x^2+17x+56=0 equation:


Simplifying
x2 + 17x + 56 = 0

Reorder the terms:
56 + 17x + x2 = 0

Solving
56 + 17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-56' to each side of the equation.
56 + 17x + -56 + x2 = 0 + -56

Reorder the terms:
56 + -56 + 17x + x2 = 0 + -56

Combine like terms: 56 + -56 = 0
0 + 17x + x2 = 0 + -56
17x + x2 = 0 + -56

Combine like terms: 0 + -56 = -56
17x + x2 = -56

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 = -56 + 72.25

Reorder the terms:
72.25 + 17x + x2 = -56 + 72.25

Combine like terms: -56 + 72.25 = 16.25
72.25 + 17x + x2 = 16.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(x + 8.5) equal to 4.031128874 and -4.031128874.

Subproblem 1

x + 8.5 = 4.031128874 Simplifying x + 8.5 = 4.031128874 Reorder the terms: 8.5 + x = 4.031128874 Solving 8.5 + x = 4.031128874 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 = 4.031128874 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 4.031128874 + -8.5 x = 4.031128874 + -8.5 Combine like terms: 4.031128874 + -8.5 = -4.468871126 x = -4.468871126 Simplifying x = -4.468871126

Subproblem 2

x + 8.5 = -4.031128874 Simplifying x + 8.5 = -4.031128874 Reorder the terms: 8.5 + x = -4.031128874 Solving 8.5 + x = -4.031128874 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 = -4.031128874 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -4.031128874 + -8.5 x = -4.031128874 + -8.5 Combine like terms: -4.031128874 + -8.5 = -12.531128874 x = -12.531128874 Simplifying x = -12.531128874

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-4.468871126, -12.531128874}

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