-x^2+20x-98=0

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Solution for -x^2+20x-98=0 equation:


Simplifying
-1x2 + 20x + -98 = 0

Reorder the terms:
-98 + 20x + -1x2 = 0

Solving
-98 + 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'.
98 + -20x + x2 = 0

Move the constant term to the right:

Add '-98' to each side of the equation.
98 + -20x + -98 + x2 = 0 + -98

Reorder the terms:
98 + -98 + -20x + x2 = 0 + -98

Combine like terms: 98 + -98 = 0
0 + -20x + x2 = 0 + -98
-20x + x2 = 0 + -98

Combine like terms: 0 + -98 = -98
-20x + x2 = -98

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 = -98 + 100

Reorder the terms:
100 + -20x + x2 = -98 + 100

Combine like terms: -98 + 100 = 2
100 + -20x + x2 = 2

Factor a perfect square on the left side:
(x + -10)(x + -10) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -10) equal to 1.414213562 and -1.414213562.

Subproblem 1

x + -10 = 1.414213562 Simplifying x + -10 = 1.414213562 Reorder the terms: -10 + x = 1.414213562 Solving -10 + x = 1.414213562 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 = 1.414213562 + 10 Combine like terms: -10 + 10 = 0 0 + x = 1.414213562 + 10 x = 1.414213562 + 10 Combine like terms: 1.414213562 + 10 = 11.414213562 x = 11.414213562 Simplifying x = 11.414213562

Subproblem 2

x + -10 = -1.414213562 Simplifying x + -10 = -1.414213562 Reorder the terms: -10 + x = -1.414213562 Solving -10 + x = -1.414213562 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 = -1.414213562 + 10 Combine like terms: -10 + 10 = 0 0 + x = -1.414213562 + 10 x = -1.414213562 + 10 Combine like terms: -1.414213562 + 10 = 8.585786438 x = 8.585786438 Simplifying x = 8.585786438

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.414213562, 8.585786438}

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