49x^2-105x-26=0

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Solution for 49x^2-105x-26=0 equation:


Simplifying
49x2 + -105x + -26 = 0

Reorder the terms:
-26 + -105x + 49x2 = 0

Solving
-26 + -105x + 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'.
-0.5306122449 + -2.142857143x + x2 = 0

Move the constant term to the right:

Add '0.5306122449' to each side of the equation.
-0.5306122449 + -2.142857143x + 0.5306122449 + x2 = 0 + 0.5306122449

Reorder the terms:
-0.5306122449 + 0.5306122449 + -2.142857143x + x2 = 0 + 0.5306122449

Combine like terms: -0.5306122449 + 0.5306122449 = 0.0000000000
0.0000000000 + -2.142857143x + x2 = 0 + 0.5306122449
-2.142857143x + x2 = 0 + 0.5306122449

Combine like terms: 0 + 0.5306122449 = 0.5306122449
-2.142857143x + x2 = 0.5306122449

The x term is -2.142857143x.  Take half its coefficient (-1.071428572).
Square it (1.147959185) and add it to both sides.

Add '1.147959185' to each side of the equation.
-2.142857143x + 1.147959185 + x2 = 0.5306122449 + 1.147959185

Reorder the terms:
1.147959185 + -2.142857143x + x2 = 0.5306122449 + 1.147959185

Combine like terms: 0.5306122449 + 1.147959185 = 1.6785714299
1.147959185 + -2.142857143x + x2 = 1.6785714299

Factor a perfect square on the left side:
(x + -1.071428572)(x + -1.071428572) = 1.6785714299

Calculate the square root of the right side: 1.29559694

Break this problem into two subproblems by setting 
(x + -1.071428572) equal to 1.29559694 and -1.29559694.

Subproblem 1

x + -1.071428572 = 1.29559694 Simplifying x + -1.071428572 = 1.29559694 Reorder the terms: -1.071428572 + x = 1.29559694 Solving -1.071428572 + x = 1.29559694 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + x = 1.29559694 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = 1.29559694 + 1.071428572 x = 1.29559694 + 1.071428572 Combine like terms: 1.29559694 + 1.071428572 = 2.367025512 x = 2.367025512 Simplifying x = 2.367025512

Subproblem 2

x + -1.071428572 = -1.29559694 Simplifying x + -1.071428572 = -1.29559694 Reorder the terms: -1.071428572 + x = -1.29559694 Solving -1.071428572 + x = -1.29559694 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + x = -1.29559694 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = -1.29559694 + 1.071428572 x = -1.29559694 + 1.071428572 Combine like terms: -1.29559694 + 1.071428572 = -0.224168368 x = -0.224168368 Simplifying x = -0.224168368

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.367025512, -0.224168368}

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