14x^2-25x-35=0

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Solution for 14x^2-25x-35=0 equation:


Simplifying
14x2 + -25x + -35 = 0

Reorder the terms:
-35 + -25x + 14x2 = 0

Solving
-35 + -25x + 14x2 = 0

Solving for variable 'x'.

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

Divide each side by '14'.
-2.5 + -1.785714286x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -1.785714286x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -1.785714286x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -1.785714286x + x2 = 0 + 2.5
-1.785714286x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-1.785714286x + x2 = 2.5

The x term is -1.785714286x.  Take half its coefficient (-0.892857143).
Square it (0.7971938778) and add it to both sides.

Add '0.7971938778' to each side of the equation.
-1.785714286x + 0.7971938778 + x2 = 2.5 + 0.7971938778

Reorder the terms:
0.7971938778 + -1.785714286x + x2 = 2.5 + 0.7971938778

Combine like terms: 2.5 + 0.7971938778 = 3.2971938778
0.7971938778 + -1.785714286x + x2 = 3.2971938778

Factor a perfect square on the left side:
(x + -0.892857143)(x + -0.892857143) = 3.2971938778

Calculate the square root of the right side: 1.815817688

Break this problem into two subproblems by setting 
(x + -0.892857143) equal to 1.815817688 and -1.815817688.

Subproblem 1

x + -0.892857143 = 1.815817688 Simplifying x + -0.892857143 = 1.815817688 Reorder the terms: -0.892857143 + x = 1.815817688 Solving -0.892857143 + x = 1.815817688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.892857143' to each side of the equation. -0.892857143 + 0.892857143 + x = 1.815817688 + 0.892857143 Combine like terms: -0.892857143 + 0.892857143 = 0.000000000 0.000000000 + x = 1.815817688 + 0.892857143 x = 1.815817688 + 0.892857143 Combine like terms: 1.815817688 + 0.892857143 = 2.708674831 x = 2.708674831 Simplifying x = 2.708674831

Subproblem 2

x + -0.892857143 = -1.815817688 Simplifying x + -0.892857143 = -1.815817688 Reorder the terms: -0.892857143 + x = -1.815817688 Solving -0.892857143 + x = -1.815817688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.892857143' to each side of the equation. -0.892857143 + 0.892857143 + x = -1.815817688 + 0.892857143 Combine like terms: -0.892857143 + 0.892857143 = 0.000000000 0.000000000 + x = -1.815817688 + 0.892857143 x = -1.815817688 + 0.892857143 Combine like terms: -1.815817688 + 0.892857143 = -0.922960545 x = -0.922960545 Simplifying x = -0.922960545

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.708674831, -0.922960545}

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