2x^2+13x=-16

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Solution for 2x^2+13x=-16 equation:


Simplifying
2x2 + 13x = -16

Reorder the terms:
13x + 2x2 = -16

Solving
13x + 2x2 = -16

Solving for variable 'x'.

Reorder the terms:
16 + 13x + 2x2 = -16 + 16

Combine like terms: -16 + 16 = 0
16 + 13x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
8 + 6.5x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 6.5x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 6.5x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 6.5x + x2 = 0 + -8
6.5x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
6.5x + x2 = -8

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = -8 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = -8 + 10.5625

Combine like terms: -8 + 10.5625 = 2.5625
10.5625 + 6.5x + x2 = 2.5625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(x + 3.25) equal to 1.600781059 and -1.600781059.

Subproblem 1

x + 3.25 = 1.600781059 Simplifying x + 3.25 = 1.600781059 Reorder the terms: 3.25 + x = 1.600781059 Solving 3.25 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 1.600781059 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 1.600781059 + -3.25 x = 1.600781059 + -3.25 Combine like terms: 1.600781059 + -3.25 = -1.649218941 x = -1.649218941 Simplifying x = -1.649218941

Subproblem 2

x + 3.25 = -1.600781059 Simplifying x + 3.25 = -1.600781059 Reorder the terms: 3.25 + x = -1.600781059 Solving 3.25 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -1.600781059 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -1.600781059 + -3.25 x = -1.600781059 + -3.25 Combine like terms: -1.600781059 + -3.25 = -4.850781059 x = -4.850781059 Simplifying x = -4.850781059

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.649218941, -4.850781059}

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