x^2+.8x-1=0

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Solution for x^2+.8x-1=0 equation:


Simplifying
x2 + 0.8x + -1 = 0

Reorder the terms:
-1 + 0.8x + x2 = 0

Solving
-1 + 0.8x + 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 + 0.8x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.8x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.8x + x2 = 0 + 1
0.8x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.8x + x2 = 1

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 1 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 1 + 0.16

Combine like terms: 1 + 0.16 = 1.16
0.16 + 0.8x + x2 = 1.16

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 1.16

Calculate the square root of the right side: 1.077032961

Break this problem into two subproblems by setting 
(x + 0.4) equal to 1.077032961 and -1.077032961.

Subproblem 1

x + 0.4 = 1.077032961 Simplifying x + 0.4 = 1.077032961 Reorder the terms: 0.4 + x = 1.077032961 Solving 0.4 + x = 1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.077032961 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.077032961 + -0.4 x = 1.077032961 + -0.4 Combine like terms: 1.077032961 + -0.4 = 0.677032961 x = 0.677032961 Simplifying x = 0.677032961

Subproblem 2

x + 0.4 = -1.077032961 Simplifying x + 0.4 = -1.077032961 Reorder the terms: 0.4 + x = -1.077032961 Solving 0.4 + x = -1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.077032961 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.077032961 + -0.4 x = -1.077032961 + -0.4 Combine like terms: -1.077032961 + -0.4 = -1.477032961 x = -1.477032961 Simplifying x = -1.477032961

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.677032961, -1.477032961}

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