4x^2+441x+729=0

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Solution for 4x^2+441x+729=0 equation:


Simplifying
4x2 + 441x + 729 = 0

Reorder the terms:
729 + 441x + 4x2 = 0

Solving
729 + 441x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
182.25 + 110.25x + x2 = 0

Move the constant term to the right:

Add '-182.25' to each side of the equation.
182.25 + 110.25x + -182.25 + x2 = 0 + -182.25

Reorder the terms:
182.25 + -182.25 + 110.25x + x2 = 0 + -182.25

Combine like terms: 182.25 + -182.25 = 0.00
0.00 + 110.25x + x2 = 0 + -182.25
110.25x + x2 = 0 + -182.25

Combine like terms: 0 + -182.25 = -182.25
110.25x + x2 = -182.25

The x term is 110.25x.  Take half its coefficient (55.125).
Square it (3038.765625) and add it to both sides.

Add '3038.765625' to each side of the equation.
110.25x + 3038.765625 + x2 = -182.25 + 3038.765625

Reorder the terms:
3038.765625 + 110.25x + x2 = -182.25 + 3038.765625

Combine like terms: -182.25 + 3038.765625 = 2856.515625
3038.765625 + 110.25x + x2 = 2856.515625

Factor a perfect square on the left side:
(x + 55.125)(x + 55.125) = 2856.515625

Calculate the square root of the right side: 53.446380841

Break this problem into two subproblems by setting 
(x + 55.125) equal to 53.446380841 and -53.446380841.

Subproblem 1

x + 55.125 = 53.446380841 Simplifying x + 55.125 = 53.446380841 Reorder the terms: 55.125 + x = 53.446380841 Solving 55.125 + x = 53.446380841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55.125' to each side of the equation. 55.125 + -55.125 + x = 53.446380841 + -55.125 Combine like terms: 55.125 + -55.125 = 0.000 0.000 + x = 53.446380841 + -55.125 x = 53.446380841 + -55.125 Combine like terms: 53.446380841 + -55.125 = -1.678619159 x = -1.678619159 Simplifying x = -1.678619159

Subproblem 2

x + 55.125 = -53.446380841 Simplifying x + 55.125 = -53.446380841 Reorder the terms: 55.125 + x = -53.446380841 Solving 55.125 + x = -53.446380841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55.125' to each side of the equation. 55.125 + -55.125 + x = -53.446380841 + -55.125 Combine like terms: 55.125 + -55.125 = 0.000 0.000 + x = -53.446380841 + -55.125 x = -53.446380841 + -55.125 Combine like terms: -53.446380841 + -55.125 = -108.571380841 x = -108.571380841 Simplifying x = -108.571380841

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.678619159, -108.571380841}

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