-3x^2-48x+4=0

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Solution for -3x^2-48x+4=0 equation:


Simplifying
-3x2 + -48x + 4 = 0

Reorder the terms:
4 + -48x + -3x2 = 0

Solving
4 + -48x + -3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-1.333333333 + 16x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 16x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 16x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 16x + x2 = 0 + 1.333333333
16x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
16x + x2 = 1.333333333

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 1.333333333 + 64

Reorder the terms:
64 + 16x + x2 = 1.333333333 + 64

Combine like terms: 1.333333333 + 64 = 65.333333333
64 + 16x + x2 = 65.333333333

Factor a perfect square on the left side:
(x + 8)(x + 8) = 65.333333333

Calculate the square root of the right side: 8.082903769

Break this problem into two subproblems by setting 
(x + 8) equal to 8.082903769 and -8.082903769.

Subproblem 1

x + 8 = 8.082903769 Simplifying x + 8 = 8.082903769 Reorder the terms: 8 + x = 8.082903769 Solving 8 + x = 8.082903769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 8.082903769 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.082903769 + -8 x = 8.082903769 + -8 Combine like terms: 8.082903769 + -8 = 0.082903769 x = 0.082903769 Simplifying x = 0.082903769

Subproblem 2

x + 8 = -8.082903769 Simplifying x + 8 = -8.082903769 Reorder the terms: 8 + x = -8.082903769 Solving 8 + x = -8.082903769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -8.082903769 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.082903769 + -8 x = -8.082903769 + -8 Combine like terms: -8.082903769 + -8 = -16.082903769 x = -16.082903769 Simplifying x = -16.082903769

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.082903769, -16.082903769}

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