2x^2-21x-1=0

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Solution for 2x^2-21x-1=0 equation:


Simplifying
2x2 + -21x + -1 = 0

Reorder the terms:
-1 + -21x + 2x2 = 0

Solving
-1 + -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'.
-0.5 + -10.5x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -10.5x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -10.5x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -10.5x + x2 = 0 + 0.5
-10.5x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-10.5x + x2 = 0.5

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 = 0.5 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = 0.5 + 27.5625

Combine like terms: 0.5 + 27.5625 = 28.0625
27.5625 + -10.5x + x2 = 28.0625

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 28.0625

Calculate the square root of the right side: 5.297405025

Break this problem into two subproblems by setting 
(x + -5.25) equal to 5.297405025 and -5.297405025.

Subproblem 1

x + -5.25 = 5.297405025 Simplifying x + -5.25 = 5.297405025 Reorder the terms: -5.25 + x = 5.297405025 Solving -5.25 + x = 5.297405025 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 = 5.297405025 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 5.297405025 + 5.25 x = 5.297405025 + 5.25 Combine like terms: 5.297405025 + 5.25 = 10.547405025 x = 10.547405025 Simplifying x = 10.547405025

Subproblem 2

x + -5.25 = -5.297405025 Simplifying x + -5.25 = -5.297405025 Reorder the terms: -5.25 + x = -5.297405025 Solving -5.25 + x = -5.297405025 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 = -5.297405025 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -5.297405025 + 5.25 x = -5.297405025 + 5.25 Combine like terms: -5.297405025 + 5.25 = -0.047405025 x = -0.047405025 Simplifying x = -0.047405025

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.547405025, -0.047405025}

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