4x^2-46x+121=0

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Solution for 4x^2-46x+121=0 equation:


Simplifying
4x2 + -46x + 121 = 0

Reorder the terms:
121 + -46x + 4x2 = 0

Solving
121 + -46x + 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'.
30.25 + -11.5x + x2 = 0

Move the constant term to the right:

Add '-30.25' to each side of the equation.
30.25 + -11.5x + -30.25 + x2 = 0 + -30.25

Reorder the terms:
30.25 + -30.25 + -11.5x + x2 = 0 + -30.25

Combine like terms: 30.25 + -30.25 = 0.00
0.00 + -11.5x + x2 = 0 + -30.25
-11.5x + x2 = 0 + -30.25

Combine like terms: 0 + -30.25 = -30.25
-11.5x + x2 = -30.25

The x term is -11.5x.  Take half its coefficient (-5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
-11.5x + 33.0625 + x2 = -30.25 + 33.0625

Reorder the terms:
33.0625 + -11.5x + x2 = -30.25 + 33.0625

Combine like terms: -30.25 + 33.0625 = 2.8125
33.0625 + -11.5x + x2 = 2.8125

Factor a perfect square on the left side:
(x + -5.75)(x + -5.75) = 2.8125

Calculate the square root of the right side: 1.677050983

Break this problem into two subproblems by setting 
(x + -5.75) equal to 1.677050983 and -1.677050983.

Subproblem 1

x + -5.75 = 1.677050983 Simplifying x + -5.75 = 1.677050983 Reorder the terms: -5.75 + x = 1.677050983 Solving -5.75 + x = 1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 1.677050983 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 1.677050983 + 5.75 x = 1.677050983 + 5.75 Combine like terms: 1.677050983 + 5.75 = 7.427050983 x = 7.427050983 Simplifying x = 7.427050983

Subproblem 2

x + -5.75 = -1.677050983 Simplifying x + -5.75 = -1.677050983 Reorder the terms: -5.75 + x = -1.677050983 Solving -5.75 + x = -1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -1.677050983 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -1.677050983 + 5.75 x = -1.677050983 + 5.75 Combine like terms: -1.677050983 + 5.75 = 4.072949017 x = 4.072949017 Simplifying x = 4.072949017

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.427050983, 4.072949017}

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