x^2-33x+58=0

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Solution for x^2-33x+58=0 equation:


Simplifying
x2 + -33x + 58 = 0

Reorder the terms:
58 + -33x + x2 = 0

Solving
58 + -33x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-58' to each side of the equation.
58 + -33x + -58 + x2 = 0 + -58

Reorder the terms:
58 + -58 + -33x + x2 = 0 + -58

Combine like terms: 58 + -58 = 0
0 + -33x + x2 = 0 + -58
-33x + x2 = 0 + -58

Combine like terms: 0 + -58 = -58
-33x + x2 = -58

The x term is -33x.  Take half its coefficient (-16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
-33x + 272.25 + x2 = -58 + 272.25

Reorder the terms:
272.25 + -33x + x2 = -58 + 272.25

Combine like terms: -58 + 272.25 = 214.25
272.25 + -33x + x2 = 214.25

Factor a perfect square on the left side:
(x + -16.5)(x + -16.5) = 214.25

Calculate the square root of the right side: 14.637281168

Break this problem into two subproblems by setting 
(x + -16.5) equal to 14.637281168 and -14.637281168.

Subproblem 1

x + -16.5 = 14.637281168 Simplifying x + -16.5 = 14.637281168 Reorder the terms: -16.5 + x = 14.637281168 Solving -16.5 + x = 14.637281168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = 14.637281168 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 14.637281168 + 16.5 x = 14.637281168 + 16.5 Combine like terms: 14.637281168 + 16.5 = 31.137281168 x = 31.137281168 Simplifying x = 31.137281168

Subproblem 2

x + -16.5 = -14.637281168 Simplifying x + -16.5 = -14.637281168 Reorder the terms: -16.5 + x = -14.637281168 Solving -16.5 + x = -14.637281168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = -14.637281168 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -14.637281168 + 16.5 x = -14.637281168 + 16.5 Combine like terms: -14.637281168 + 16.5 = 1.862718832 x = 1.862718832 Simplifying x = 1.862718832

Solution

The solution to the problem is based on the solutions from the subproblems. x = {31.137281168, 1.862718832}

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