x^2+16x=-3

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Solution for x^2+16x=-3 equation:


Simplifying
x2 + 16x = -3

Reorder the terms:
16x + x2 = -3

Solving
16x + x2 = -3

Solving for variable 'x'.

Reorder the terms:
3 + 16x + x2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 16x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 16x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 16x + x2 = 0 + -3
16x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
16x + x2 = -3

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 = -3 + 64

Reorder the terms:
64 + 16x + x2 = -3 + 64

Combine like terms: -3 + 64 = 61
64 + 16x + x2 = 61

Factor a perfect square on the left side:
(x + 8)(x + 8) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(x + 8) equal to 7.810249676 and -7.810249676.

Subproblem 1

x + 8 = 7.810249676 Simplifying x + 8 = 7.810249676 Reorder the terms: 8 + x = 7.810249676 Solving 8 + x = 7.810249676 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 = 7.810249676 + -8 Combine like terms: 8 + -8 = 0 0 + x = 7.810249676 + -8 x = 7.810249676 + -8 Combine like terms: 7.810249676 + -8 = -0.189750324 x = -0.189750324 Simplifying x = -0.189750324

Subproblem 2

x + 8 = -7.810249676 Simplifying x + 8 = -7.810249676 Reorder the terms: 8 + x = -7.810249676 Solving 8 + x = -7.810249676 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 = -7.810249676 + -8 Combine like terms: 8 + -8 = 0 0 + x = -7.810249676 + -8 x = -7.810249676 + -8 Combine like terms: -7.810249676 + -8 = -15.810249676 x = -15.810249676 Simplifying x = -15.810249676

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.189750324, -15.810249676}

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