29x+108x^2-72=0

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Solution for 29x+108x^2-72=0 equation:


Simplifying
29x + 108x2 + -72 = 0

Reorder the terms:
-72 + 29x + 108x2 = 0

Solving
-72 + 29x + 108x2 = 0

Solving for variable 'x'.

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

Divide each side by '108'.
-0.6666666667 + 0.2685185185x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 0.2685185185x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 0.2685185185x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 0.2685185185x + x2 = 0 + 0.6666666667
0.2685185185x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
0.2685185185x + x2 = 0.6666666667

The x term is 0.2685185185x.  Take half its coefficient (0.1342592593).
Square it (0.01802554871) and add it to both sides.

Add '0.01802554871' to each side of the equation.
0.2685185185x + 0.01802554871 + x2 = 0.6666666667 + 0.01802554871

Reorder the terms:
0.01802554871 + 0.2685185185x + x2 = 0.6666666667 + 0.01802554871

Combine like terms: 0.6666666667 + 0.01802554871 = 0.68469221541
0.01802554871 + 0.2685185185x + x2 = 0.68469221541

Factor a perfect square on the left side:
(x + 0.1342592593)(x + 0.1342592593) = 0.68469221541

Calculate the square root of the right side: 0.827461308

Break this problem into two subproblems by setting 
(x + 0.1342592593) equal to 0.827461308 and -0.827461308.

Subproblem 1

x + 0.1342592593 = 0.827461308 Simplifying x + 0.1342592593 = 0.827461308 Reorder the terms: 0.1342592593 + x = 0.827461308 Solving 0.1342592593 + x = 0.827461308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1342592593' to each side of the equation. 0.1342592593 + -0.1342592593 + x = 0.827461308 + -0.1342592593 Combine like terms: 0.1342592593 + -0.1342592593 = 0.0000000000 0.0000000000 + x = 0.827461308 + -0.1342592593 x = 0.827461308 + -0.1342592593 Combine like terms: 0.827461308 + -0.1342592593 = 0.6932020487 x = 0.6932020487 Simplifying x = 0.6932020487

Subproblem 2

x + 0.1342592593 = -0.827461308 Simplifying x + 0.1342592593 = -0.827461308 Reorder the terms: 0.1342592593 + x = -0.827461308 Solving 0.1342592593 + x = -0.827461308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1342592593' to each side of the equation. 0.1342592593 + -0.1342592593 + x = -0.827461308 + -0.1342592593 Combine like terms: 0.1342592593 + -0.1342592593 = 0.0000000000 0.0000000000 + x = -0.827461308 + -0.1342592593 x = -0.827461308 + -0.1342592593 Combine like terms: -0.827461308 + -0.1342592593 = -0.9617205673 x = -0.9617205673 Simplifying x = -0.9617205673

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.6932020487, -0.9617205673}

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