x^2+16x=-42

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Solution for x^2+16x=-42 equation:


Simplifying
x2 + 16x = -42

Reorder the terms:
16x + x2 = -42

Solving
16x + x2 = -42

Solving for variable 'x'.

Reorder the terms:
42 + 16x + x2 = -42 + 42

Combine like terms: -42 + 42 = 0
42 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + 16x + -42 + x2 = 0 + -42

Reorder the terms:
42 + -42 + 16x + x2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + 16x + x2 = 0 + -42
16x + x2 = 0 + -42

Combine like terms: 0 + -42 = -42
16x + x2 = -42

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 = -42 + 64

Reorder the terms:
64 + 16x + x2 = -42 + 64

Combine like terms: -42 + 64 = 22
64 + 16x + x2 = 22

Factor a perfect square on the left side:
(x + 8)(x + 8) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(x + 8) equal to 4.69041576 and -4.69041576.

Subproblem 1

x + 8 = 4.69041576 Simplifying x + 8 = 4.69041576 Reorder the terms: 8 + x = 4.69041576 Solving 8 + x = 4.69041576 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 = 4.69041576 + -8 Combine like terms: 8 + -8 = 0 0 + x = 4.69041576 + -8 x = 4.69041576 + -8 Combine like terms: 4.69041576 + -8 = -3.30958424 x = -3.30958424 Simplifying x = -3.30958424

Subproblem 2

x + 8 = -4.69041576 Simplifying x + 8 = -4.69041576 Reorder the terms: 8 + x = -4.69041576 Solving 8 + x = -4.69041576 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 = -4.69041576 + -8 Combine like terms: 8 + -8 = 0 0 + x = -4.69041576 + -8 x = -4.69041576 + -8 Combine like terms: -4.69041576 + -8 = -12.69041576 x = -12.69041576 Simplifying x = -12.69041576

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.30958424, -12.69041576}

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