x^2-.833x-1=0

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Solution for x^2-.833x-1=0 equation:


Simplifying
x2 + -0.833x + -1 = 0

Reorder the terms:
-1 + -0.833x + x2 = 0

Solving
-1 + -0.833x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.833x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.833x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.833x + x2 = 0 + 1
-0.833x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.833x + x2 = 1

The x term is -0.833x.  Take half its coefficient (-0.4165).
Square it (0.17347225) and add it to both sides.

Add '0.17347225' to each side of the equation.
-0.833x + 0.17347225 + x2 = 1 + 0.17347225

Reorder the terms:
0.17347225 + -0.833x + x2 = 1 + 0.17347225

Combine like terms: 1 + 0.17347225 = 1.17347225
0.17347225 + -0.833x + x2 = 1.17347225

Factor a perfect square on the left side:
(x + -0.4165)(x + -0.4165) = 1.17347225

Calculate the square root of the right side: 1.083269242

Break this problem into two subproblems by setting 
(x + -0.4165) equal to 1.083269242 and -1.083269242.

Subproblem 1

x + -0.4165 = 1.083269242 Simplifying x + -0.4165 = 1.083269242 Reorder the terms: -0.4165 + x = 1.083269242 Solving -0.4165 + x = 1.083269242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4165' to each side of the equation. -0.4165 + 0.4165 + x = 1.083269242 + 0.4165 Combine like terms: -0.4165 + 0.4165 = 0.0000 0.0000 + x = 1.083269242 + 0.4165 x = 1.083269242 + 0.4165 Combine like terms: 1.083269242 + 0.4165 = 1.499769242 x = 1.499769242 Simplifying x = 1.499769242

Subproblem 2

x + -0.4165 = -1.083269242 Simplifying x + -0.4165 = -1.083269242 Reorder the terms: -0.4165 + x = -1.083269242 Solving -0.4165 + x = -1.083269242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4165' to each side of the equation. -0.4165 + 0.4165 + x = -1.083269242 + 0.4165 Combine like terms: -0.4165 + 0.4165 = 0.0000 0.0000 + x = -1.083269242 + 0.4165 x = -1.083269242 + 0.4165 Combine like terms: -1.083269242 + 0.4165 = -0.666769242 x = -0.666769242 Simplifying x = -0.666769242

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.499769242, -0.666769242}

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