-x^2+20x-81=0

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Solution for -x^2+20x-81=0 equation:


Simplifying
-1x2 + 20x + -81 = 0

Reorder the terms:
-81 + 20x + -1x2 = 0

Solving
-81 + 20x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
81 + -20x + x2 = 0

Move the constant term to the right:

Add '-81' to each side of the equation.
81 + -20x + -81 + x2 = 0 + -81

Reorder the terms:
81 + -81 + -20x + x2 = 0 + -81

Combine like terms: 81 + -81 = 0
0 + -20x + x2 = 0 + -81
-20x + x2 = 0 + -81

Combine like terms: 0 + -81 = -81
-20x + x2 = -81

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -81 + 100

Reorder the terms:
100 + -20x + x2 = -81 + 100

Combine like terms: -81 + 100 = 19
100 + -20x + x2 = 19

Factor a perfect square on the left side:
(x + -10)(x + -10) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + -10) equal to 4.358898944 and -4.358898944.

Subproblem 1

x + -10 = 4.358898944 Simplifying x + -10 = 4.358898944 Reorder the terms: -10 + x = 4.358898944 Solving -10 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 4.358898944 + 10 Combine like terms: -10 + 10 = 0 0 + x = 4.358898944 + 10 x = 4.358898944 + 10 Combine like terms: 4.358898944 + 10 = 14.358898944 x = 14.358898944 Simplifying x = 14.358898944

Subproblem 2

x + -10 = -4.358898944 Simplifying x + -10 = -4.358898944 Reorder the terms: -10 + x = -4.358898944 Solving -10 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -4.358898944 + 10 Combine like terms: -10 + 10 = 0 0 + x = -4.358898944 + 10 x = -4.358898944 + 10 Combine like terms: -4.358898944 + 10 = 5.641101056 x = 5.641101056 Simplifying x = 5.641101056

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.358898944, 5.641101056}

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