49x^2-28x-108=0

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Solution for 49x^2-28x-108=0 equation:


Simplifying
49x2 + -28x + -108 = 0

Reorder the terms:
-108 + -28x + 49x2 = 0

Solving
-108 + -28x + 49x2 = 0

Solving for variable 'x'.

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

Divide each side by '49'.
-2.204081633 + -0.5714285714x + x2 = 0

Move the constant term to the right:

Add '2.204081633' to each side of the equation.
-2.204081633 + -0.5714285714x + 2.204081633 + x2 = 0 + 2.204081633

Reorder the terms:
-2.204081633 + 2.204081633 + -0.5714285714x + x2 = 0 + 2.204081633

Combine like terms: -2.204081633 + 2.204081633 = 0.000000000
0.000000000 + -0.5714285714x + x2 = 0 + 2.204081633
-0.5714285714x + x2 = 0 + 2.204081633

Combine like terms: 0 + 2.204081633 = 2.204081633
-0.5714285714x + x2 = 2.204081633

The x term is -0.5714285714x.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714x + 0.08163265305 + x2 = 2.204081633 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714x + x2 = 2.204081633 + 0.08163265305

Combine like terms: 2.204081633 + 0.08163265305 = 2.28571428605
0.08163265305 + -0.5714285714x + x2 = 2.28571428605

Factor a perfect square on the left side:
(x + -0.2857142857)(x + -0.2857142857) = 2.28571428605

Calculate the square root of the right side: 1.511857892

Break this problem into two subproblems by setting 
(x + -0.2857142857) equal to 1.511857892 and -1.511857892.

Subproblem 1

x + -0.2857142857 = 1.511857892 Simplifying x + -0.2857142857 = 1.511857892 Reorder the terms: -0.2857142857 + x = 1.511857892 Solving -0.2857142857 + x = 1.511857892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 1.511857892 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 1.511857892 + 0.2857142857 x = 1.511857892 + 0.2857142857 Combine like terms: 1.511857892 + 0.2857142857 = 1.7975721777 x = 1.7975721777 Simplifying x = 1.7975721777

Subproblem 2

x + -0.2857142857 = -1.511857892 Simplifying x + -0.2857142857 = -1.511857892 Reorder the terms: -0.2857142857 + x = -1.511857892 Solving -0.2857142857 + x = -1.511857892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -1.511857892 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -1.511857892 + 0.2857142857 x = -1.511857892 + 0.2857142857 Combine like terms: -1.511857892 + 0.2857142857 = -1.2261436063 x = -1.2261436063 Simplifying x = -1.2261436063

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.7975721777, -1.2261436063}

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