5x^2=51x+54

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Solution for 5x^2=51x+54 equation:


Simplifying
5x2 = 51x + 54

Reorder the terms:
5x2 = 54 + 51x

Solving
5x2 = 54 + 51x

Solving for variable 'x'.

Reorder the terms:
-54 + -51x + 5x2 = 54 + 51x + -54 + -51x

Reorder the terms:
-54 + -51x + 5x2 = 54 + -54 + 51x + -51x

Combine like terms: 54 + -54 = 0
-54 + -51x + 5x2 = 0 + 51x + -51x
-54 + -51x + 5x2 = 51x + -51x

Combine like terms: 51x + -51x = 0
-54 + -51x + 5x2 = 0

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

Divide each side by '5'.
-10.8 + -10.2x + x2 = 0

Move the constant term to the right:

Add '10.8' to each side of the equation.
-10.8 + -10.2x + 10.8 + x2 = 0 + 10.8

Reorder the terms:
-10.8 + 10.8 + -10.2x + x2 = 0 + 10.8

Combine like terms: -10.8 + 10.8 = 0.0
0.0 + -10.2x + x2 = 0 + 10.8
-10.2x + x2 = 0 + 10.8

Combine like terms: 0 + 10.8 = 10.8
-10.2x + x2 = 10.8

The x term is -10.2x.  Take half its coefficient (-5.1).
Square it (26.01) and add it to both sides.

Add '26.01' to each side of the equation.
-10.2x + 26.01 + x2 = 10.8 + 26.01

Reorder the terms:
26.01 + -10.2x + x2 = 10.8 + 26.01

Combine like terms: 10.8 + 26.01 = 36.81
26.01 + -10.2x + x2 = 36.81

Factor a perfect square on the left side:
(x + -5.1)(x + -5.1) = 36.81

Calculate the square root of the right side: 6.067124525

Break this problem into two subproblems by setting 
(x + -5.1) equal to 6.067124525 and -6.067124525.

Subproblem 1

x + -5.1 = 6.067124525 Simplifying x + -5.1 = 6.067124525 Reorder the terms: -5.1 + x = 6.067124525 Solving -5.1 + x = 6.067124525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.1' to each side of the equation. -5.1 + 5.1 + x = 6.067124525 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + x = 6.067124525 + 5.1 x = 6.067124525 + 5.1 Combine like terms: 6.067124525 + 5.1 = 11.167124525 x = 11.167124525 Simplifying x = 11.167124525

Subproblem 2

x + -5.1 = -6.067124525 Simplifying x + -5.1 = -6.067124525 Reorder the terms: -5.1 + x = -6.067124525 Solving -5.1 + x = -6.067124525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.1' to each side of the equation. -5.1 + 5.1 + x = -6.067124525 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + x = -6.067124525 + 5.1 x = -6.067124525 + 5.1 Combine like terms: -6.067124525 + 5.1 = -0.967124525 x = -0.967124525 Simplifying x = -0.967124525

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.167124525, -0.967124525}

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