6x^2-48=.12x

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Solution for 6x^2-48=.12x equation:


Simplifying
6x2 + -48 = 0.12x

Reorder the terms:
-48 + 6x2 = 0.12x

Solving
-48 + 6x2 = 0.12x

Solving for variable 'x'.

Reorder the terms:
-48 + -0.12x + 6x2 = 0.12x + -0.12x

Combine like terms: 0.12x + -0.12x = 0.00
-48 + -0.12x + 6x2 = 0.00

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

Divide each side by '6'.
-8 + -0.02x + x2 = 0.00

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -0.02x + 8 + x2 = 0.00 + 8

Reorder the terms:
-8 + 8 + -0.02x + x2 = 0.00 + 8

Combine like terms: -8 + 8 = 0
0 + -0.02x + x2 = 0.00 + 8
-0.02x + x2 = 0.00 + 8

Combine like terms: 0.00 + 8 = 8
-0.02x + x2 = 8

The x term is -0.02x.  Take half its coefficient (-0.01).
Square it (0.0001) and add it to both sides.

Add '0.0001' to each side of the equation.
-0.02x + 0.0001 + x2 = 8 + 0.0001

Reorder the terms:
0.0001 + -0.02x + x2 = 8 + 0.0001

Combine like terms: 8 + 0.0001 = 8.0001
0.0001 + -0.02x + x2 = 8.0001

Factor a perfect square on the left side:
(x + -0.01)(x + -0.01) = 8.0001

Calculate the square root of the right side: 2.828444802

Break this problem into two subproblems by setting 
(x + -0.01) equal to 2.828444802 and -2.828444802.

Subproblem 1

x + -0.01 = 2.828444802 Simplifying x + -0.01 = 2.828444802 Reorder the terms: -0.01 + x = 2.828444802 Solving -0.01 + x = 2.828444802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01' to each side of the equation. -0.01 + 0.01 + x = 2.828444802 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + x = 2.828444802 + 0.01 x = 2.828444802 + 0.01 Combine like terms: 2.828444802 + 0.01 = 2.838444802 x = 2.838444802 Simplifying x = 2.838444802

Subproblem 2

x + -0.01 = -2.828444802 Simplifying x + -0.01 = -2.828444802 Reorder the terms: -0.01 + x = -2.828444802 Solving -0.01 + x = -2.828444802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01' to each side of the equation. -0.01 + 0.01 + x = -2.828444802 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + x = -2.828444802 + 0.01 x = -2.828444802 + 0.01 Combine like terms: -2.828444802 + 0.01 = -2.818444802 x = -2.818444802 Simplifying x = -2.818444802

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.838444802, -2.818444802}

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