4x^2-41x=73

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Solution for 4x^2-41x=73 equation:


Simplifying
4x2 + -41x = 73

Reorder the terms:
-41x + 4x2 = 73

Solving
-41x + 4x2 = 73

Solving for variable 'x'.

Reorder the terms:
-73 + -41x + 4x2 = 73 + -73

Combine like terms: 73 + -73 = 0
-73 + -41x + 4x2 = 0

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

Divide each side by '4'.
-18.25 + -10.25x + x2 = 0

Move the constant term to the right:

Add '18.25' to each side of the equation.
-18.25 + -10.25x + 18.25 + x2 = 0 + 18.25

Reorder the terms:
-18.25 + 18.25 + -10.25x + x2 = 0 + 18.25

Combine like terms: -18.25 + 18.25 = 0.00
0.00 + -10.25x + x2 = 0 + 18.25
-10.25x + x2 = 0 + 18.25

Combine like terms: 0 + 18.25 = 18.25
-10.25x + x2 = 18.25

The x term is -10.25x.  Take half its coefficient (-5.125).
Square it (26.265625) and add it to both sides.

Add '26.265625' to each side of the equation.
-10.25x + 26.265625 + x2 = 18.25 + 26.265625

Reorder the terms:
26.265625 + -10.25x + x2 = 18.25 + 26.265625

Combine like terms: 18.25 + 26.265625 = 44.515625
26.265625 + -10.25x + x2 = 44.515625

Factor a perfect square on the left side:
(x + -5.125)(x + -5.125) = 44.515625

Calculate the square root of the right side: 6.672003073

Break this problem into two subproblems by setting 
(x + -5.125) equal to 6.672003073 and -6.672003073.

Subproblem 1

x + -5.125 = 6.672003073 Simplifying x + -5.125 = 6.672003073 Reorder the terms: -5.125 + x = 6.672003073 Solving -5.125 + x = 6.672003073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = 6.672003073 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = 6.672003073 + 5.125 x = 6.672003073 + 5.125 Combine like terms: 6.672003073 + 5.125 = 11.797003073 x = 11.797003073 Simplifying x = 11.797003073

Subproblem 2

x + -5.125 = -6.672003073 Simplifying x + -5.125 = -6.672003073 Reorder the terms: -5.125 + x = -6.672003073 Solving -5.125 + x = -6.672003073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = -6.672003073 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = -6.672003073 + 5.125 x = -6.672003073 + 5.125 Combine like terms: -6.672003073 + 5.125 = -1.547003073 x = -1.547003073 Simplifying x = -1.547003073

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.797003073, -1.547003073}

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