2x^2-21x-392=0

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Solution for 2x^2-21x-392=0 equation:


Simplifying
2x2 + -21x + -392 = 0

Reorder the terms:
-392 + -21x + 2x2 = 0

Solving
-392 + -21x + 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'.
-196 + -10.5x + x2 = 0

Move the constant term to the right:

Add '196' to each side of the equation.
-196 + -10.5x + 196 + x2 = 0 + 196

Reorder the terms:
-196 + 196 + -10.5x + x2 = 0 + 196

Combine like terms: -196 + 196 = 0
0 + -10.5x + x2 = 0 + 196
-10.5x + x2 = 0 + 196

Combine like terms: 0 + 196 = 196
-10.5x + x2 = 196

The x term is -10.5x.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5x + 27.5625 + x2 = 196 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = 196 + 27.5625

Combine like terms: 196 + 27.5625 = 223.5625
27.5625 + -10.5x + x2 = 223.5625

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 223.5625

Calculate the square root of the right side: 14.952006554

Break this problem into two subproblems by setting 
(x + -5.25) equal to 14.952006554 and -14.952006554.

Subproblem 1

x + -5.25 = 14.952006554 Simplifying x + -5.25 = 14.952006554 Reorder the terms: -5.25 + x = 14.952006554 Solving -5.25 + x = 14.952006554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 14.952006554 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 14.952006554 + 5.25 x = 14.952006554 + 5.25 Combine like terms: 14.952006554 + 5.25 = 20.202006554 x = 20.202006554 Simplifying x = 20.202006554

Subproblem 2

x + -5.25 = -14.952006554 Simplifying x + -5.25 = -14.952006554 Reorder the terms: -5.25 + x = -14.952006554 Solving -5.25 + x = -14.952006554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -14.952006554 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -14.952006554 + 5.25 x = -14.952006554 + 5.25 Combine like terms: -14.952006554 + 5.25 = -9.702006554 x = -9.702006554 Simplifying x = -9.702006554

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.202006554, -9.702006554}

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