5x^2-3x-5400=0

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Solution for 5x^2-3x-5400=0 equation:


Simplifying
5x2 + -3x + -5400 = 0

Reorder the terms:
-5400 + -3x + 5x2 = 0

Solving
-5400 + -3x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-1080 + -0.6x + x2 = 0

Move the constant term to the right:

Add '1080' to each side of the equation.
-1080 + -0.6x + 1080 + x2 = 0 + 1080

Reorder the terms:
-1080 + 1080 + -0.6x + x2 = 0 + 1080

Combine like terms: -1080 + 1080 = 0
0 + -0.6x + x2 = 0 + 1080
-0.6x + x2 = 0 + 1080

Combine like terms: 0 + 1080 = 1080
-0.6x + x2 = 1080

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 1080 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 1080 + 0.09

Combine like terms: 1080 + 0.09 = 1080.09
0.09 + -0.6x + x2 = 1080.09

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 1080.09

Calculate the square root of the right side: 32.864722728

Break this problem into two subproblems by setting 
(x + -0.3) equal to 32.864722728 and -32.864722728.

Subproblem 1

x + -0.3 = 32.864722728 Simplifying x + -0.3 = 32.864722728 Reorder the terms: -0.3 + x = 32.864722728 Solving -0.3 + x = 32.864722728 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 32.864722728 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 32.864722728 + 0.3 x = 32.864722728 + 0.3 Combine like terms: 32.864722728 + 0.3 = 33.164722728 x = 33.164722728 Simplifying x = 33.164722728

Subproblem 2

x + -0.3 = -32.864722728 Simplifying x + -0.3 = -32.864722728 Reorder the terms: -0.3 + x = -32.864722728 Solving -0.3 + x = -32.864722728 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -32.864722728 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -32.864722728 + 0.3 x = -32.864722728 + 0.3 Combine like terms: -32.864722728 + 0.3 = -32.564722728 x = -32.564722728 Simplifying x = -32.564722728

Solution

The solution to the problem is based on the solutions from the subproblems. x = {33.164722728, -32.564722728}

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