49x^2+28x-6=0

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Solution for 49x^2+28x-6=0 equation:


Simplifying
49x2 + 28x + -6 = 0

Reorder the terms:
-6 + 28x + 49x2 = 0

Solving
-6 + 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'.
-0.1224489796 + 0.5714285714x + x2 = 0

Move the constant term to the right:

Add '0.1224489796' to each side of the equation.
-0.1224489796 + 0.5714285714x + 0.1224489796 + x2 = 0 + 0.1224489796

Reorder the terms:
-0.1224489796 + 0.1224489796 + 0.5714285714x + x2 = 0 + 0.1224489796

Combine like terms: -0.1224489796 + 0.1224489796 = 0.0000000000
0.0000000000 + 0.5714285714x + x2 = 0 + 0.1224489796
0.5714285714x + x2 = 0 + 0.1224489796

Combine like terms: 0 + 0.1224489796 = 0.1224489796
0.5714285714x + x2 = 0.1224489796

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 = 0.1224489796 + 0.08163265305

Reorder the terms:
0.08163265305 + 0.5714285714x + x2 = 0.1224489796 + 0.08163265305

Combine like terms: 0.1224489796 + 0.08163265305 = 0.20408163265
0.08163265305 + 0.5714285714x + x2 = 0.20408163265

Factor a perfect square on the left side:
(x + 0.2857142857)(x + 0.2857142857) = 0.20408163265

Calculate the square root of the right side: 0.451753951

Break this problem into two subproblems by setting 
(x + 0.2857142857) equal to 0.451753951 and -0.451753951.

Subproblem 1

x + 0.2857142857 = 0.451753951 Simplifying x + 0.2857142857 = 0.451753951 Reorder the terms: 0.2857142857 + x = 0.451753951 Solving 0.2857142857 + x = 0.451753951 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 = 0.451753951 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 0.451753951 + -0.2857142857 x = 0.451753951 + -0.2857142857 Combine like terms: 0.451753951 + -0.2857142857 = 0.1660396653 x = 0.1660396653 Simplifying x = 0.1660396653

Subproblem 2

x + 0.2857142857 = -0.451753951 Simplifying x + 0.2857142857 = -0.451753951 Reorder the terms: 0.2857142857 + x = -0.451753951 Solving 0.2857142857 + x = -0.451753951 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 = -0.451753951 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -0.451753951 + -0.2857142857 x = -0.451753951 + -0.2857142857 Combine like terms: -0.451753951 + -0.2857142857 = -0.7374682367 x = -0.7374682367 Simplifying x = -0.7374682367

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1660396653, -0.7374682367}

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