18x^2-73x+59=0

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Solution for 18x^2-73x+59=0 equation:


Simplifying
18x2 + -73x + 59 = 0

Reorder the terms:
59 + -73x + 18x2 = 0

Solving
59 + -73x + 18x2 = 0

Solving for variable 'x'.

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

Divide each side by '18'.
3.277777778 + -4.055555556x + x2 = 0

Move the constant term to the right:

Add '-3.277777778' to each side of the equation.
3.277777778 + -4.055555556x + -3.277777778 + x2 = 0 + -3.277777778

Reorder the terms:
3.277777778 + -3.277777778 + -4.055555556x + x2 = 0 + -3.277777778

Combine like terms: 3.277777778 + -3.277777778 = 0.000000000
0.000000000 + -4.055555556x + x2 = 0 + -3.277777778
-4.055555556x + x2 = 0 + -3.277777778

Combine like terms: 0 + -3.277777778 = -3.277777778
-4.055555556x + x2 = -3.277777778

The x term is -4.055555556x.  Take half its coefficient (-2.027777778).
Square it (4.111882717) and add it to both sides.

Add '4.111882717' to each side of the equation.
-4.055555556x + 4.111882717 + x2 = -3.277777778 + 4.111882717

Reorder the terms:
4.111882717 + -4.055555556x + x2 = -3.277777778 + 4.111882717

Combine like terms: -3.277777778 + 4.111882717 = 0.834104939
4.111882717 + -4.055555556x + x2 = 0.834104939

Factor a perfect square on the left side:
(x + -2.027777778)(x + -2.027777778) = 0.834104939

Calculate the square root of the right side: 0.913293457

Break this problem into two subproblems by setting 
(x + -2.027777778) equal to 0.913293457 and -0.913293457.

Subproblem 1

x + -2.027777778 = 0.913293457 Simplifying x + -2.027777778 = 0.913293457 Reorder the terms: -2.027777778 + x = 0.913293457 Solving -2.027777778 + x = 0.913293457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.027777778' to each side of the equation. -2.027777778 + 2.027777778 + x = 0.913293457 + 2.027777778 Combine like terms: -2.027777778 + 2.027777778 = 0.000000000 0.000000000 + x = 0.913293457 + 2.027777778 x = 0.913293457 + 2.027777778 Combine like terms: 0.913293457 + 2.027777778 = 2.941071235 x = 2.941071235 Simplifying x = 2.941071235

Subproblem 2

x + -2.027777778 = -0.913293457 Simplifying x + -2.027777778 = -0.913293457 Reorder the terms: -2.027777778 + x = -0.913293457 Solving -2.027777778 + x = -0.913293457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.027777778' to each side of the equation. -2.027777778 + 2.027777778 + x = -0.913293457 + 2.027777778 Combine like terms: -2.027777778 + 2.027777778 = 0.000000000 0.000000000 + x = -0.913293457 + 2.027777778 x = -0.913293457 + 2.027777778 Combine like terms: -0.913293457 + 2.027777778 = 1.114484321 x = 1.114484321 Simplifying x = 1.114484321

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.941071235, 1.114484321}

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