x^2-81x+49=0

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Solution for x^2-81x+49=0 equation:


Simplifying
x2 + -81x + 49 = 0

Reorder the terms:
49 + -81x + x2 = 0

Solving
49 + -81x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + -81x + -49 + x2 = 0 + -49

Reorder the terms:
49 + -49 + -81x + x2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + -81x + x2 = 0 + -49
-81x + x2 = 0 + -49

Combine like terms: 0 + -49 = -49
-81x + x2 = -49

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 = -49 + 1640.25

Reorder the terms:
1640.25 + -81x + x2 = -49 + 1640.25

Combine like terms: -49 + 1640.25 = 1591.25
1640.25 + -81x + x2 = 1591.25

Factor a perfect square on the left side:
(x + -40.5)(x + -40.5) = 1591.25

Calculate the square root of the right side: 39.890475054

Break this problem into two subproblems by setting 
(x + -40.5) equal to 39.890475054 and -39.890475054.

Subproblem 1

x + -40.5 = 39.890475054 Simplifying x + -40.5 = 39.890475054 Reorder the terms: -40.5 + x = 39.890475054 Solving -40.5 + x = 39.890475054 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 = 39.890475054 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = 39.890475054 + 40.5 x = 39.890475054 + 40.5 Combine like terms: 39.890475054 + 40.5 = 80.390475054 x = 80.390475054 Simplifying x = 80.390475054

Subproblem 2

x + -40.5 = -39.890475054 Simplifying x + -40.5 = -39.890475054 Reorder the terms: -40.5 + x = -39.890475054 Solving -40.5 + x = -39.890475054 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 = -39.890475054 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = -39.890475054 + 40.5 x = -39.890475054 + 40.5 Combine like terms: -39.890475054 + 40.5 = 0.609524946 x = 0.609524946 Simplifying x = 0.609524946

Solution

The solution to the problem is based on the solutions from the subproblems. x = {80.390475054, 0.609524946}

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