x^2-81x+81=17

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Solution for x^2-81x+81=17 equation:


Simplifying
x2 + -81x + 81 = 17

Reorder the terms:
81 + -81x + x2 = 17

Solving
81 + -81x + x2 = 17

Solving for variable 'x'.

Reorder the terms:
81 + -17 + -81x + x2 = 17 + -17

Combine like terms: 81 + -17 = 64
64 + -81x + x2 = 17 + -17

Combine like terms: 17 + -17 = 0
64 + -81x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-64' to each side of the equation.
64 + -81x + -64 + x2 = 0 + -64

Reorder the terms:
64 + -64 + -81x + x2 = 0 + -64

Combine like terms: 64 + -64 = 0
0 + -81x + x2 = 0 + -64
-81x + x2 = 0 + -64

Combine like terms: 0 + -64 = -64
-81x + x2 = -64

The x term is -81x.  Take half its coefficient (-40.5).
Square it (1640.25) and add it to both sides.

Add '1640.25' to each side of the equation.
-81x + 1640.25 + x2 = -64 + 1640.25

Reorder the terms:
1640.25 + -81x + x2 = -64 + 1640.25

Combine like terms: -64 + 1640.25 = 1576.25
1640.25 + -81x + x2 = 1576.25

Factor a perfect square on the left side:
(x + -40.5)(x + -40.5) = 1576.25

Calculate the square root of the right side: 39.702015062

Break this problem into two subproblems by setting 
(x + -40.5) equal to 39.702015062 and -39.702015062.

Subproblem 1

x + -40.5 = 39.702015062 Simplifying x + -40.5 = 39.702015062 Reorder the terms: -40.5 + x = 39.702015062 Solving -40.5 + x = 39.702015062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.5' to each side of the equation. -40.5 + 40.5 + x = 39.702015062 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = 39.702015062 + 40.5 x = 39.702015062 + 40.5 Combine like terms: 39.702015062 + 40.5 = 80.202015062 x = 80.202015062 Simplifying x = 80.202015062

Subproblem 2

x + -40.5 = -39.702015062 Simplifying x + -40.5 = -39.702015062 Reorder the terms: -40.5 + x = -39.702015062 Solving -40.5 + x = -39.702015062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.5' to each side of the equation. -40.5 + 40.5 + x = -39.702015062 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = -39.702015062 + 40.5 x = -39.702015062 + 40.5 Combine like terms: -39.702015062 + 40.5 = 0.797984938 x = 0.797984938 Simplifying x = 0.797984938

Solution

The solution to the problem is based on the solutions from the subproblems. x = {80.202015062, 0.797984938}

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