4x^2-41x+46=0

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Solution for 4x^2-41x+46=0 equation:


Simplifying
4x2 + -41x + 46 = 0

Reorder the terms:
46 + -41x + 4x2 = 0

Solving
46 + -41x + 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'.
11.5 + -10.25x + x2 = 0

Move the constant term to the right:

Add '-11.5' to each side of the equation.
11.5 + -10.25x + -11.5 + x2 = 0 + -11.5

Reorder the terms:
11.5 + -11.5 + -10.25x + x2 = 0 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + -10.25x + x2 = 0 + -11.5
-10.25x + x2 = 0 + -11.5

Combine like terms: 0 + -11.5 = -11.5
-10.25x + x2 = -11.5

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 = -11.5 + 26.265625

Reorder the terms:
26.265625 + -10.25x + x2 = -11.5 + 26.265625

Combine like terms: -11.5 + 26.265625 = 14.765625
26.265625 + -10.25x + x2 = 14.765625

Factor a perfect square on the left side:
(x + -5.125)(x + -5.125) = 14.765625

Calculate the square root of the right side: 3.842606537

Break this problem into two subproblems by setting 
(x + -5.125) equal to 3.842606537 and -3.842606537.

Subproblem 1

x + -5.125 = 3.842606537 Simplifying x + -5.125 = 3.842606537 Reorder the terms: -5.125 + x = 3.842606537 Solving -5.125 + x = 3.842606537 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 = 3.842606537 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = 3.842606537 + 5.125 x = 3.842606537 + 5.125 Combine like terms: 3.842606537 + 5.125 = 8.967606537 x = 8.967606537 Simplifying x = 8.967606537

Subproblem 2

x + -5.125 = -3.842606537 Simplifying x + -5.125 = -3.842606537 Reorder the terms: -5.125 + x = -3.842606537 Solving -5.125 + x = -3.842606537 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 = -3.842606537 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = -3.842606537 + 5.125 x = -3.842606537 + 5.125 Combine like terms: -3.842606537 + 5.125 = 1.282393463 x = 1.282393463 Simplifying x = 1.282393463

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.967606537, 1.282393463}

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