2x^2-14x-49=0

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Solution for 2x^2-14x-49=0 equation:


Simplifying
2x2 + -14x + -49 = 0

Reorder the terms:
-49 + -14x + 2x2 = 0

Solving
-49 + -14x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-24.5 + -7x + x2 = 0

Move the constant term to the right:

Add '24.5' to each side of the equation.
-24.5 + -7x + 24.5 + x2 = 0 + 24.5

Reorder the terms:
-24.5 + 24.5 + -7x + x2 = 0 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + -7x + x2 = 0 + 24.5
-7x + x2 = 0 + 24.5

Combine like terms: 0 + 24.5 = 24.5
-7x + x2 = 24.5

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 24.5 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 24.5 + 12.25

Combine like terms: 24.5 + 12.25 = 36.75
12.25 + -7x + x2 = 36.75

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 36.75

Calculate the square root of the right side: 6.062177826

Break this problem into two subproblems by setting 
(x + -3.5) equal to 6.062177826 and -6.062177826.

Subproblem 1

x + -3.5 = 6.062177826 Simplifying x + -3.5 = 6.062177826 Reorder the terms: -3.5 + x = 6.062177826 Solving -3.5 + x = 6.062177826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 6.062177826 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 6.062177826 + 3.5 x = 6.062177826 + 3.5 Combine like terms: 6.062177826 + 3.5 = 9.562177826 x = 9.562177826 Simplifying x = 9.562177826

Subproblem 2

x + -3.5 = -6.062177826 Simplifying x + -3.5 = -6.062177826 Reorder the terms: -3.5 + x = -6.062177826 Solving -3.5 + x = -6.062177826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -6.062177826 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -6.062177826 + 3.5 x = -6.062177826 + 3.5 Combine like terms: -6.062177826 + 3.5 = -2.562177826 x = -2.562177826 Simplifying x = -2.562177826

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.562177826, -2.562177826}

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