4x^2-45x+54=0

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Solution for 4x^2-45x+54=0 equation:


Simplifying
4x2 + -45x + 54 = 0

Reorder the terms:
54 + -45x + 4x2 = 0

Solving
54 + -45x + 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'.
13.5 + -11.25x + x2 = 0

Move the constant term to the right:

Add '-13.5' to each side of the equation.
13.5 + -11.25x + -13.5 + x2 = 0 + -13.5

Reorder the terms:
13.5 + -13.5 + -11.25x + x2 = 0 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + -11.25x + x2 = 0 + -13.5
-11.25x + x2 = 0 + -13.5

Combine like terms: 0 + -13.5 = -13.5
-11.25x + x2 = -13.5

The x term is -11.25x.  Take half its coefficient (-5.625).
Square it (31.640625) and add it to both sides.

Add '31.640625' to each side of the equation.
-11.25x + 31.640625 + x2 = -13.5 + 31.640625

Reorder the terms:
31.640625 + -11.25x + x2 = -13.5 + 31.640625

Combine like terms: -13.5 + 31.640625 = 18.140625
31.640625 + -11.25x + x2 = 18.140625

Factor a perfect square on the left side:
(x + -5.625)(x + -5.625) = 18.140625

Calculate the square root of the right side: 4.259181259

Break this problem into two subproblems by setting 
(x + -5.625) equal to 4.259181259 and -4.259181259.

Subproblem 1

x + -5.625 = 4.259181259 Simplifying x + -5.625 = 4.259181259 Reorder the terms: -5.625 + x = 4.259181259 Solving -5.625 + x = 4.259181259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = 4.259181259 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = 4.259181259 + 5.625 x = 4.259181259 + 5.625 Combine like terms: 4.259181259 + 5.625 = 9.884181259 x = 9.884181259 Simplifying x = 9.884181259

Subproblem 2

x + -5.625 = -4.259181259 Simplifying x + -5.625 = -4.259181259 Reorder the terms: -5.625 + x = -4.259181259 Solving -5.625 + x = -4.259181259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = -4.259181259 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = -4.259181259 + 5.625 x = -4.259181259 + 5.625 Combine like terms: -4.259181259 + 5.625 = 1.365818741 x = 1.365818741 Simplifying x = 1.365818741

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.884181259, 1.365818741}

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