2x^2-1=11x

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Solution for 2x^2-1=11x equation:


Simplifying
2x2 + -1 = 11x

Reorder the terms:
-1 + 2x2 = 11x

Solving
-1 + 2x2 = 11x

Solving for variable 'x'.

Reorder the terms:
-1 + -11x + 2x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
-1 + -11x + 2x2 = 0

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

Divide each side by '2'.
-0.5 + -5.5x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -5.5x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -5.5x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -5.5x + x2 = 0 + 0.5
-5.5x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-5.5x + x2 = 0.5

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 0.5 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 0.5 + 7.5625

Combine like terms: 0.5 + 7.5625 = 8.0625
7.5625 + -5.5x + x2 = 8.0625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(x + -2.75) equal to 2.839454173 and -2.839454173.

Subproblem 1

x + -2.75 = 2.839454173 Simplifying x + -2.75 = 2.839454173 Reorder the terms: -2.75 + x = 2.839454173 Solving -2.75 + x = 2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.839454173 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.839454173 + 2.75 x = 2.839454173 + 2.75 Combine like terms: 2.839454173 + 2.75 = 5.589454173 x = 5.589454173 Simplifying x = 5.589454173

Subproblem 2

x + -2.75 = -2.839454173 Simplifying x + -2.75 = -2.839454173 Reorder the terms: -2.75 + x = -2.839454173 Solving -2.75 + x = -2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.839454173 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.839454173 + 2.75 x = -2.839454173 + 2.75 Combine like terms: -2.839454173 + 2.75 = -0.089454173 x = -0.089454173 Simplifying x = -0.089454173

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.589454173, -0.089454173}

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