2x^2+13x-16=0

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Solution for 2x^2+13x-16=0 equation:


Simplifying
2x2 + 13x + -16 = 0

Reorder the terms:
-16 + 13x + 2x2 = 0

Solving
-16 + 13x + 2x2 = 0

Solving for variable 'x'.

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 = 18.5625
10.5625 + 6.5x + x2 = 18.5625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 18.5625

Calculate the square root of the right side: 4.308421985

Break this problem into two subproblems by setting 
(x + 3.25) equal to 4.308421985 and -4.308421985.

Subproblem 1

x + 3.25 = 4.308421985 Simplifying x + 3.25 = 4.308421985 Reorder the terms: 3.25 + x = 4.308421985 Solving 3.25 + x = 4.308421985 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 = 4.308421985 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 4.308421985 + -3.25 x = 4.308421985 + -3.25 Combine like terms: 4.308421985 + -3.25 = 1.058421985 x = 1.058421985 Simplifying x = 1.058421985

Subproblem 2

x + 3.25 = -4.308421985 Simplifying x + 3.25 = -4.308421985 Reorder the terms: 3.25 + x = -4.308421985 Solving 3.25 + x = -4.308421985 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 = -4.308421985 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -4.308421985 + -3.25 x = -4.308421985 + -3.25 Combine like terms: -4.308421985 + -3.25 = -7.558421985 x = -7.558421985 Simplifying x = -7.558421985

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.058421985, -7.558421985}

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