2x^2-13x-14=0

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Solution for 2x^2-13x-14=0 equation:


Simplifying
2x2 + -13x + -14 = 0

Reorder the terms:
-14 + -13x + 2x2 = 0

Solving
-14 + -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'.
-7 + -6.5x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -6.5x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -6.5x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6.5x + x2 = 0 + 7
-6.5x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-6.5x + x2 = 7

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 = 7 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 7 + 10.5625

Combine like terms: 7 + 10.5625 = 17.5625
10.5625 + -6.5x + x2 = 17.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 17.5625

Calculate the square root of the right side: 4.190763654

Break this problem into two subproblems by setting 
(x + -3.25) equal to 4.190763654 and -4.190763654.

Subproblem 1

x + -3.25 = 4.190763654 Simplifying x + -3.25 = 4.190763654 Reorder the terms: -3.25 + x = 4.190763654 Solving -3.25 + x = 4.190763654 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 = 4.190763654 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 4.190763654 + 3.25 x = 4.190763654 + 3.25 Combine like terms: 4.190763654 + 3.25 = 7.440763654 x = 7.440763654 Simplifying x = 7.440763654

Subproblem 2

x + -3.25 = -4.190763654 Simplifying x + -3.25 = -4.190763654 Reorder the terms: -3.25 + x = -4.190763654 Solving -3.25 + x = -4.190763654 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 = -4.190763654 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -4.190763654 + 3.25 x = -4.190763654 + 3.25 Combine like terms: -4.190763654 + 3.25 = -0.940763654 x = -0.940763654 Simplifying x = -0.940763654

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.440763654, -0.940763654}

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