2x^2-4x-5=6

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Solution for 2x^2-4x-5=6 equation:


Simplifying
2x2 + -4x + -5 = 6

Reorder the terms:
-5 + -4x + 2x2 = 6

Solving
-5 + -4x + 2x2 = 6

Solving for variable 'x'.

Reorder the terms:
-5 + -6 + -4x + 2x2 = 6 + -6

Combine like terms: -5 + -6 = -11
-11 + -4x + 2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-11 + -4x + 2x2 = 0

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

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

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -2x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -2x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -2x + x2 = 0 + 5.5
-2x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-2x + x2 = 5.5

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 5.5 + 1

Reorder the terms:
1 + -2x + x2 = 5.5 + 1

Combine like terms: 5.5 + 1 = 6.5
1 + -2x + x2 = 6.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 6.5

Calculate the square root of the right side: 2.549509757

Break this problem into two subproblems by setting 
(x + -1) equal to 2.549509757 and -2.549509757.

Subproblem 1

x + -1 = 2.549509757 Simplifying x + -1 = 2.549509757 Reorder the terms: -1 + x = 2.549509757 Solving -1 + x = 2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.549509757 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.549509757 + 1 x = 2.549509757 + 1 Combine like terms: 2.549509757 + 1 = 3.549509757 x = 3.549509757 Simplifying x = 3.549509757

Subproblem 2

x + -1 = -2.549509757 Simplifying x + -1 = -2.549509757 Reorder the terms: -1 + x = -2.549509757 Solving -1 + x = -2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.549509757 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.549509757 + 1 x = -2.549509757 + 1 Combine like terms: -2.549509757 + 1 = -1.549509757 x = -1.549509757 Simplifying x = -1.549509757

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.549509757, -1.549509757}

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