0.3x^2-6x-18=0

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Solution for 0.3x^2-6x-18=0 equation:


Simplifying
0.3x2 + -6x + -18 = 0

Reorder the terms:
-18 + -6x + 0.3x2 = 0

Solving
-18 + -6x + 0.3x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.3'.
-60 + -20x + x2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -20x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + -20x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -20x + x2 = 0 + 60
-20x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
-20x + x2 = 60

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = 60 + 100

Reorder the terms:
100 + -20x + x2 = 60 + 100

Combine like terms: 60 + 100 = 160
100 + -20x + x2 = 160

Factor a perfect square on the left side:
(x + -10)(x + -10) = 160

Calculate the square root of the right side: 12.649110641

Break this problem into two subproblems by setting 
(x + -10) equal to 12.649110641 and -12.649110641.

Subproblem 1

x + -10 = 12.649110641 Simplifying x + -10 = 12.649110641 Reorder the terms: -10 + x = 12.649110641 Solving -10 + x = 12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 12.649110641 + 10 Combine like terms: -10 + 10 = 0 0 + x = 12.649110641 + 10 x = 12.649110641 + 10 Combine like terms: 12.649110641 + 10 = 22.649110641 x = 22.649110641 Simplifying x = 22.649110641

Subproblem 2

x + -10 = -12.649110641 Simplifying x + -10 = -12.649110641 Reorder the terms: -10 + x = -12.649110641 Solving -10 + x = -12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -12.649110641 + 10 Combine like terms: -10 + 10 = 0 0 + x = -12.649110641 + 10 x = -12.649110641 + 10 Combine like terms: -12.649110641 + 10 = -2.649110641 x = -2.649110641 Simplifying x = -2.649110641

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.649110641, -2.649110641}

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