2x^2+13x-140=0

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Solution for 2x^2+13x-140=0 equation:


Simplifying
2x2 + 13x + -140 = 0

Reorder the terms:
-140 + 13x + 2x2 = 0

Solving
-140 + 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'.
-70 + 6.5x + x2 = 0

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 6.5x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + 6.5x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 6.5x + x2 = 0 + 70
6.5x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
6.5x + x2 = 70

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 = 70 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 70 + 10.5625

Combine like terms: 70 + 10.5625 = 80.5625
10.5625 + 6.5x + x2 = 80.5625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 80.5625

Calculate the square root of the right side: 8.975661536

Break this problem into two subproblems by setting 
(x + 3.25) equal to 8.975661536 and -8.975661536.

Subproblem 1

x + 3.25 = 8.975661536 Simplifying x + 3.25 = 8.975661536 Reorder the terms: 3.25 + x = 8.975661536 Solving 3.25 + x = 8.975661536 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 = 8.975661536 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 8.975661536 + -3.25 x = 8.975661536 + -3.25 Combine like terms: 8.975661536 + -3.25 = 5.725661536 x = 5.725661536 Simplifying x = 5.725661536

Subproblem 2

x + 3.25 = -8.975661536 Simplifying x + 3.25 = -8.975661536 Reorder the terms: 3.25 + x = -8.975661536 Solving 3.25 + x = -8.975661536 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 = -8.975661536 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -8.975661536 + -3.25 x = -8.975661536 + -3.25 Combine like terms: -8.975661536 + -3.25 = -12.225661536 x = -12.225661536 Simplifying x = -12.225661536

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.725661536, -12.225661536}

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