862x^2+x-0.05=0

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Solution for 862x^2+x-0.05=0 equation:


Simplifying
862x2 + x + -0.05 = 0

Reorder the terms:
-0.05 + x + 862x2 = 0

Solving
-0.05 + x + 862x2 = 0

Solving for variable 'x'.

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

Divide each side by '862'.
-0.00005800464037 + 0.001160092807x + x2 = 0

Move the constant term to the right:

Add '0.00005800464037' to each side of the equation.
-0.00005800464037 + 0.001160092807x + 0.00005800464037 + x2 = 0 + 0.00005800464037

Reorder the terms:
-0.00005800464037 + 0.00005800464037 + 0.001160092807x + x2 = 0 + 0.00005800464037

Combine like terms: -0.00005800464037 + 0.00005800464037 = 0.00000000000000
0.00000000000000 + 0.001160092807x + x2 = 0 + 0.00005800464037
0.001160092807x + x2 = 0 + 0.00005800464037

Combine like terms: 0 + 0.00005800464037 = 0.00005800464037
0.001160092807x + x2 = 0.00005800464037

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.001160092807x + 0.25 + x2 = 0.00005800464037 + 0.25

Reorder the terms:
0.25 + 0.001160092807x + x2 = 0.00005800464037 + 0.25

Combine like terms: 0.00005800464037 + 0.25 = 0.25005800464037
0.25 + 0.001160092807x + x2 = 0.25005800464037

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.25005800464037

Calculate the square root of the right side: 0.500058001

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.500058001 and -0.500058001.

Subproblem 1

x + 0.5 = 0.500058001 Simplifying x + 0.5 = 0.500058001 Reorder the terms: 0.5 + x = 0.500058001 Solving 0.5 + x = 0.500058001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.500058001 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.500058001 + -0.5 x = 0.500058001 + -0.5 Combine like terms: 0.500058001 + -0.5 = 0.000058001 x = 0.000058001 Simplifying x = 0.000058001

Subproblem 2

x + 0.5 = -0.500058001 Simplifying x + 0.5 = -0.500058001 Reorder the terms: 0.5 + x = -0.500058001 Solving 0.5 + x = -0.500058001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.500058001 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.500058001 + -0.5 x = -0.500058001 + -0.5 Combine like terms: -0.500058001 + -0.5 = -1.000058001 x = -1.000058001 Simplifying x = -1.000058001

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.000058001, -1.000058001}

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