2x^2+14x-627=0

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Solution for 2x^2+14x-627=0 equation:


Simplifying
2x2 + 14x + -627 = 0

Reorder the terms:
-627 + 14x + 2x2 = 0

Solving
-627 + 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'.
-313.5 + 7x + x2 = 0

Move the constant term to the right:

Add '313.5' to each side of the equation.
-313.5 + 7x + 313.5 + x2 = 0 + 313.5

Reorder the terms:
-313.5 + 313.5 + 7x + x2 = 0 + 313.5

Combine like terms: -313.5 + 313.5 = 0.0
0.0 + 7x + x2 = 0 + 313.5
7x + x2 = 0 + 313.5

Combine like terms: 0 + 313.5 = 313.5
7x + x2 = 313.5

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 = 313.5 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 313.5 + 12.25

Combine like terms: 313.5 + 12.25 = 325.75
12.25 + 7x + x2 = 325.75

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 325.75

Calculate the square root of the right side: 18.048545648

Break this problem into two subproblems by setting 
(x + 3.5) equal to 18.048545648 and -18.048545648.

Subproblem 1

x + 3.5 = 18.048545648 Simplifying x + 3.5 = 18.048545648 Reorder the terms: 3.5 + x = 18.048545648 Solving 3.5 + x = 18.048545648 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 = 18.048545648 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 18.048545648 + -3.5 x = 18.048545648 + -3.5 Combine like terms: 18.048545648 + -3.5 = 14.548545648 x = 14.548545648 Simplifying x = 14.548545648

Subproblem 2

x + 3.5 = -18.048545648 Simplifying x + 3.5 = -18.048545648 Reorder the terms: 3.5 + x = -18.048545648 Solving 3.5 + x = -18.048545648 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 = -18.048545648 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -18.048545648 + -3.5 x = -18.048545648 + -3.5 Combine like terms: -18.048545648 + -3.5 = -21.548545648 x = -21.548545648 Simplifying x = -21.548545648

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.548545648, -21.548545648}

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