x^2+16x+57=0

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Solution for x^2+16x+57=0 equation:


Simplifying
x2 + 16x + 57 = 0

Reorder the terms:
57 + 16x + x2 = 0

Solving
57 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-57' to each side of the equation.
57 + 16x + -57 + x2 = 0 + -57

Reorder the terms:
57 + -57 + 16x + x2 = 0 + -57

Combine like terms: 57 + -57 = 0
0 + 16x + x2 = 0 + -57
16x + x2 = 0 + -57

Combine like terms: 0 + -57 = -57
16x + x2 = -57

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -57 + 64

Reorder the terms:
64 + 16x + x2 = -57 + 64

Combine like terms: -57 + 64 = 7
64 + 16x + x2 = 7

Factor a perfect square on the left side:
(x + 8)(x + 8) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 8) equal to 2.645751311 and -2.645751311.

Subproblem 1

x + 8 = 2.645751311 Simplifying x + 8 = 2.645751311 Reorder the terms: 8 + x = 2.645751311 Solving 8 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 2.645751311 + -8 Combine like terms: 8 + -8 = 0 0 + x = 2.645751311 + -8 x = 2.645751311 + -8 Combine like terms: 2.645751311 + -8 = -5.354248689 x = -5.354248689 Simplifying x = -5.354248689

Subproblem 2

x + 8 = -2.645751311 Simplifying x + 8 = -2.645751311 Reorder the terms: 8 + x = -2.645751311 Solving 8 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -2.645751311 + -8 Combine like terms: 8 + -8 = 0 0 + x = -2.645751311 + -8 x = -2.645751311 + -8 Combine like terms: -2.645751311 + -8 = -10.645751311 x = -10.645751311 Simplifying x = -10.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-5.354248689, -10.645751311}

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