2x^2-7x-88=0

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Solution for 2x^2-7x-88=0 equation:


Simplifying
2x2 + -7x + -88 = 0

Reorder the terms:
-88 + -7x + 2x2 = 0

Solving
-88 + -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'.
-44 + -3.5x + x2 = 0

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + -3.5x + 44 + x2 = 0 + 44

Reorder the terms:
-44 + 44 + -3.5x + x2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + -3.5x + x2 = 0 + 44
-3.5x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
-3.5x + x2 = 44

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 = 44 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 44 + 3.0625

Combine like terms: 44 + 3.0625 = 47.0625
3.0625 + -3.5x + x2 = 47.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 47.0625

Calculate the square root of the right side: 6.860211367

Break this problem into two subproblems by setting 
(x + -1.75) equal to 6.860211367 and -6.860211367.

Subproblem 1

x + -1.75 = 6.860211367 Simplifying x + -1.75 = 6.860211367 Reorder the terms: -1.75 + x = 6.860211367 Solving -1.75 + x = 6.860211367 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 = 6.860211367 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 6.860211367 + 1.75 x = 6.860211367 + 1.75 Combine like terms: 6.860211367 + 1.75 = 8.610211367 x = 8.610211367 Simplifying x = 8.610211367

Subproblem 2

x + -1.75 = -6.860211367 Simplifying x + -1.75 = -6.860211367 Reorder the terms: -1.75 + x = -6.860211367 Solving -1.75 + x = -6.860211367 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 = -6.860211367 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -6.860211367 + 1.75 x = -6.860211367 + 1.75 Combine like terms: -6.860211367 + 1.75 = -5.110211367 x = -5.110211367 Simplifying x = -5.110211367

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.610211367, -5.110211367}

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