2x^2+13x-3=0

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Solution for 2x^2+13x-3=0 equation:


Simplifying
2x2 + 13x + -3 = 0

Reorder the terms:
-3 + 13x + 2x2 = 0

Solving
-3 + 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'.
-1.5 + 6.5x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 6.5x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 6.5x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 6.5x + x2 = 0 + 1.5
6.5x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
6.5x + x2 = 1.5

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 = 1.5 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 1.5 + 10.5625

Combine like terms: 1.5 + 10.5625 = 12.0625
10.5625 + 6.5x + x2 = 12.0625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 12.0625

Calculate the square root of the right side: 3.473110997

Break this problem into two subproblems by setting 
(x + 3.25) equal to 3.473110997 and -3.473110997.

Subproblem 1

x + 3.25 = 3.473110997 Simplifying x + 3.25 = 3.473110997 Reorder the terms: 3.25 + x = 3.473110997 Solving 3.25 + x = 3.473110997 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 = 3.473110997 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.473110997 + -3.25 x = 3.473110997 + -3.25 Combine like terms: 3.473110997 + -3.25 = 0.223110997 x = 0.223110997 Simplifying x = 0.223110997

Subproblem 2

x + 3.25 = -3.473110997 Simplifying x + 3.25 = -3.473110997 Reorder the terms: 3.25 + x = -3.473110997 Solving 3.25 + x = -3.473110997 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 = -3.473110997 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.473110997 + -3.25 x = -3.473110997 + -3.25 Combine like terms: -3.473110997 + -3.25 = -6.723110997 x = -6.723110997 Simplifying x = -6.723110997

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.223110997, -6.723110997}

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