(2x^2)+7x-16=0

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Solution for (2x^2)+7x-16=0 equation: 


Simplifying
(2x2) + 7x + -16 = 0

Reorder the terms:
-16 + 7x + (2x2) = 0

Solving
-16 + 7x + (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 + 3.5x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 3.5x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 3.5x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3.5x + x2 = 0 + 8
3.5x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
3.5x + x2 = 8

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 8 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 8 + 3.0625

Combine like terms: 8 + 3.0625 = 11.0625
3.0625 + 3.5x + x2 = 11.0625

Factor a perfect square on the left side:
((x) + 1.75)((x) + 1.75) = 11.0625

Calculate the square root of the right side: 3.326033674

Break this problem into two subproblems by setting 
((x) + 1.75) equal to 3.326033674 and -3.326033674.


Subproblem 1
(x) + 1.75 = 3.326033674

Simplifying
(x) + 1.75 = 3.326033674
x + 1.75 = 3.326033674

Reorder the terms:
1.75 + x = 3.326033674

Solving
1.75 + x = 3.326033674

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 3.326033674 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 3.326033674 + -1.75
x = 3.326033674 + -1.75

Combine like terms: 3.326033674 + -1.75 = 1.576033674
x = 1.576033674

Simplifying
x = 1.576033674


Subproblem 2
(x) + 1.75 = -3.326033674

Simplifying
(x) + 1.75 = -3.326033674
x + 1.75 = -3.326033674

Reorder the terms:
1.75 + x = -3.326033674

Solving
1.75 + x = -3.326033674

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -3.326033674 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -3.326033674 + -1.75
x = -3.326033674 + -1.75

Combine like terms: -3.326033674 + -1.75 = -5.076033674
x = -5.076033674

Simplifying
x = -5.076033674


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.576033674, -5.076033674}

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