6x^2+13x-20=0

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Solution for 6x^2+13x-20=0 equation:


Simplifying
6x2 + 13x + -20 = 0

Reorder the terms:
-20 + 13x + 6x2 = 0

Solving
-20 + 13x + 6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-3.333333333 + 2.166666667x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 2.166666667x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 2.166666667x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 2.166666667x + x2 = 0 + 3.333333333
2.166666667x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
2.166666667x + x2 = 3.333333333

The x term is 2.166666667x.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667x + 1.173611113 + x2 = 3.333333333 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667x + x2 = 3.333333333 + 1.173611113

Combine like terms: 3.333333333 + 1.173611113 = 4.506944446
1.173611113 + 2.166666667x + x2 = 4.506944446

Factor a perfect square on the left side:
(x + 1.083333334)(x + 1.083333334) = 4.506944446

Calculate the square root of the right side: 2.122956534

Break this problem into two subproblems by setting 
(x + 1.083333334) equal to 2.122956534 and -2.122956534.

Subproblem 1

x + 1.083333334 = 2.122956534 Simplifying x + 1.083333334 = 2.122956534 Reorder the terms: 1.083333334 + x = 2.122956534 Solving 1.083333334 + x = 2.122956534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = 2.122956534 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 2.122956534 + -1.083333334 x = 2.122956534 + -1.083333334 Combine like terms: 2.122956534 + -1.083333334 = 1.0396232 x = 1.0396232 Simplifying x = 1.0396232

Subproblem 2

x + 1.083333334 = -2.122956534 Simplifying x + 1.083333334 = -2.122956534 Reorder the terms: 1.083333334 + x = -2.122956534 Solving 1.083333334 + x = -2.122956534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = -2.122956534 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -2.122956534 + -1.083333334 x = -2.122956534 + -1.083333334 Combine like terms: -2.122956534 + -1.083333334 = -3.206289868 x = -3.206289868 Simplifying x = -3.206289868

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.0396232, -3.206289868}

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