2x^2+x-16=0

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


Simplifying
2x2 + x + -16 = 0

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

Solving
-16 + x + 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 + 0.5x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 0.5x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 0.5x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 0.5x + x2 = 0 + 8
0.5x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
0.5x + x2 = 8

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5x + 0.25 + x2 = 8 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
0.25 + 0.5x + x2 = 8.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.872281323 and -2.872281323.

Subproblem 1

x + 0.5 = 2.872281323 Simplifying x + 0.5 = 2.872281323 Reorder the terms: 0.5 + x = 2.872281323 Solving 0.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.872281323 + -0.5 x = 2.872281323 + -0.5 Combine like terms: 2.872281323 + -0.5 = 2.372281323 x = 2.372281323 Simplifying x = 2.372281323

Subproblem 2

x + 0.5 = -2.872281323 Simplifying x + 0.5 = -2.872281323 Reorder the terms: 0.5 + x = -2.872281323 Solving 0.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.872281323 + -0.5 x = -2.872281323 + -0.5 Combine like terms: -2.872281323 + -0.5 = -3.372281323 x = -3.372281323 Simplifying x = -3.372281323

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.372281323, -3.372281323}

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