x^2-0.83x-0.83=0

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Solution for x^2-0.83x-0.83=0 equation:


Simplifying
x2 + -0.83x + -0.83 = 0

Reorder the terms:
-0.83 + -0.83x + x2 = 0

Solving
-0.83 + -0.83x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.83' to each side of the equation.
-0.83 + -0.83x + 0.83 + x2 = 0 + 0.83

Reorder the terms:
-0.83 + 0.83 + -0.83x + x2 = 0 + 0.83

Combine like terms: -0.83 + 0.83 = 0.00
0.00 + -0.83x + x2 = 0 + 0.83
-0.83x + x2 = 0 + 0.83

Combine like terms: 0 + 0.83 = 0.83
-0.83x + x2 = 0.83

The x term is -0.83x.  Take half its coefficient (-0.415).
Square it (0.172225) and add it to both sides.

Add '0.172225' to each side of the equation.
-0.83x + 0.172225 + x2 = 0.83 + 0.172225

Reorder the terms:
0.172225 + -0.83x + x2 = 0.83 + 0.172225

Combine like terms: 0.83 + 0.172225 = 1.002225
0.172225 + -0.83x + x2 = 1.002225

Factor a perfect square on the left side:
(x + -0.415)(x + -0.415) = 1.002225

Calculate the square root of the right side: 1.001111882

Break this problem into two subproblems by setting 
(x + -0.415) equal to 1.001111882 and -1.001111882.

Subproblem 1

x + -0.415 = 1.001111882 Simplifying x + -0.415 = 1.001111882 Reorder the terms: -0.415 + x = 1.001111882 Solving -0.415 + x = 1.001111882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.415' to each side of the equation. -0.415 + 0.415 + x = 1.001111882 + 0.415 Combine like terms: -0.415 + 0.415 = 0.000 0.000 + x = 1.001111882 + 0.415 x = 1.001111882 + 0.415 Combine like terms: 1.001111882 + 0.415 = 1.416111882 x = 1.416111882 Simplifying x = 1.416111882

Subproblem 2

x + -0.415 = -1.001111882 Simplifying x + -0.415 = -1.001111882 Reorder the terms: -0.415 + x = -1.001111882 Solving -0.415 + x = -1.001111882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.415' to each side of the equation. -0.415 + 0.415 + x = -1.001111882 + 0.415 Combine like terms: -0.415 + 0.415 = 0.000 0.000 + x = -1.001111882 + 0.415 x = -1.001111882 + 0.415 Combine like terms: -1.001111882 + 0.415 = -0.586111882 x = -0.586111882 Simplifying x = -0.586111882

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.416111882, -0.586111882}

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