3x^2-87x+364=0

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Solution for 3x^2-87x+364=0 equation:


Simplifying
3x2 + -87x + 364 = 0

Reorder the terms:
364 + -87x + 3x2 = 0

Solving
364 + -87x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
121.3333333 + -29x + x2 = 0

Move the constant term to the right:

Add '-121.3333333' to each side of the equation.
121.3333333 + -29x + -121.3333333 + x2 = 0 + -121.3333333

Reorder the terms:
121.3333333 + -121.3333333 + -29x + x2 = 0 + -121.3333333

Combine like terms: 121.3333333 + -121.3333333 = 0.0000000
0.0000000 + -29x + x2 = 0 + -121.3333333
-29x + x2 = 0 + -121.3333333

Combine like terms: 0 + -121.3333333 = -121.3333333
-29x + x2 = -121.3333333

The x term is -29x.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29x + 210.25 + x2 = -121.3333333 + 210.25

Reorder the terms:
210.25 + -29x + x2 = -121.3333333 + 210.25

Combine like terms: -121.3333333 + 210.25 = 88.9166667
210.25 + -29x + x2 = 88.9166667

Factor a perfect square on the left side:
(x + -14.5)(x + -14.5) = 88.9166667

Calculate the square root of the right side: 9.429563442

Break this problem into two subproblems by setting 
(x + -14.5) equal to 9.429563442 and -9.429563442.

Subproblem 1

x + -14.5 = 9.429563442 Simplifying x + -14.5 = 9.429563442 Reorder the terms: -14.5 + x = 9.429563442 Solving -14.5 + x = 9.429563442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 9.429563442 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 9.429563442 + 14.5 x = 9.429563442 + 14.5 Combine like terms: 9.429563442 + 14.5 = 23.929563442 x = 23.929563442 Simplifying x = 23.929563442

Subproblem 2

x + -14.5 = -9.429563442 Simplifying x + -14.5 = -9.429563442 Reorder the terms: -14.5 + x = -9.429563442 Solving -14.5 + x = -9.429563442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -9.429563442 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -9.429563442 + 14.5 x = -9.429563442 + 14.5 Combine like terms: -9.429563442 + 14.5 = 5.070436558 x = 5.070436558 Simplifying x = 5.070436558

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.929563442, 5.070436558}

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