5x^2-58x+100=0

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Solution for 5x^2-58x+100=0 equation:


Simplifying
5x2 + -58x + 100 = 0

Reorder the terms:
100 + -58x + 5x2 = 0

Solving
100 + -58x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
20 + -11.6x + x2 = 0

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -11.6x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -11.6x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -11.6x + x2 = 0 + -20
-11.6x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-11.6x + x2 = -20

The x term is -11.6x.  Take half its coefficient (-5.8).
Square it (33.64) and add it to both sides.

Add '33.64' to each side of the equation.
-11.6x + 33.64 + x2 = -20 + 33.64

Reorder the terms:
33.64 + -11.6x + x2 = -20 + 33.64

Combine like terms: -20 + 33.64 = 13.64
33.64 + -11.6x + x2 = 13.64

Factor a perfect square on the left side:
(x + -5.8)(x + -5.8) = 13.64

Calculate the square root of the right side: 3.693237063

Break this problem into two subproblems by setting 
(x + -5.8) equal to 3.693237063 and -3.693237063.

Subproblem 1

x + -5.8 = 3.693237063 Simplifying x + -5.8 = 3.693237063 Reorder the terms: -5.8 + x = 3.693237063 Solving -5.8 + x = 3.693237063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.8' to each side of the equation. -5.8 + 5.8 + x = 3.693237063 + 5.8 Combine like terms: -5.8 + 5.8 = 0.0 0.0 + x = 3.693237063 + 5.8 x = 3.693237063 + 5.8 Combine like terms: 3.693237063 + 5.8 = 9.493237063 x = 9.493237063 Simplifying x = 9.493237063

Subproblem 2

x + -5.8 = -3.693237063 Simplifying x + -5.8 = -3.693237063 Reorder the terms: -5.8 + x = -3.693237063 Solving -5.8 + x = -3.693237063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.8' to each side of the equation. -5.8 + 5.8 + x = -3.693237063 + 5.8 Combine like terms: -5.8 + 5.8 = 0.0 0.0 + x = -3.693237063 + 5.8 x = -3.693237063 + 5.8 Combine like terms: -3.693237063 + 5.8 = 2.106762937 x = 2.106762937 Simplifying x = 2.106762937

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.493237063, 2.106762937}

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