10x^2-x-81=0

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Solution for 10x^2-x-81=0 equation:


Simplifying
10x2 + -1x + -81 = 0

Reorder the terms:
-81 + -1x + 10x2 = 0

Solving
-81 + -1x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
-8.1 + -0.1x + x2 = 0

Move the constant term to the right:

Add '8.1' to each side of the equation.
-8.1 + -0.1x + 8.1 + x2 = 0 + 8.1

Reorder the terms:
-8.1 + 8.1 + -0.1x + x2 = 0 + 8.1

Combine like terms: -8.1 + 8.1 = 0.0
0.0 + -0.1x + x2 = 0 + 8.1
-0.1x + x2 = 0 + 8.1

Combine like terms: 0 + 8.1 = 8.1
-0.1x + x2 = 8.1

The x term is -0.1x.  Take half its coefficient (-0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
-0.1x + 0.0025 + x2 = 8.1 + 0.0025

Reorder the terms:
0.0025 + -0.1x + x2 = 8.1 + 0.0025

Combine like terms: 8.1 + 0.0025 = 8.1025
0.0025 + -0.1x + x2 = 8.1025

Factor a perfect square on the left side:
(x + -0.05)(x + -0.05) = 8.1025

Calculate the square root of the right side: 2.846489065

Break this problem into two subproblems by setting 
(x + -0.05) equal to 2.846489065 and -2.846489065.

Subproblem 1

x + -0.05 = 2.846489065 Simplifying x + -0.05 = 2.846489065 Reorder the terms: -0.05 + x = 2.846489065 Solving -0.05 + x = 2.846489065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 2.846489065 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 2.846489065 + 0.05 x = 2.846489065 + 0.05 Combine like terms: 2.846489065 + 0.05 = 2.896489065 x = 2.896489065 Simplifying x = 2.896489065

Subproblem 2

x + -0.05 = -2.846489065 Simplifying x + -0.05 = -2.846489065 Reorder the terms: -0.05 + x = -2.846489065 Solving -0.05 + x = -2.846489065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -2.846489065 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -2.846489065 + 0.05 x = -2.846489065 + 0.05 Combine like terms: -2.846489065 + 0.05 = -2.796489065 x = -2.796489065 Simplifying x = -2.796489065

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.896489065, -2.796489065}

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