6x^2-3x-46=-8

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Solution for 6x^2-3x-46=-8 equation:


Simplifying
6x2 + -3x + -46 = -8

Reorder the terms:
-46 + -3x + 6x2 = -8

Solving
-46 + -3x + 6x2 = -8

Solving for variable 'x'.

Reorder the terms:
-46 + 8 + -3x + 6x2 = -8 + 8

Combine like terms: -46 + 8 = -38
-38 + -3x + 6x2 = -8 + 8

Combine like terms: -8 + 8 = 0
-38 + -3x + 6x2 = 0

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

Divide each side by '6'.
-6.333333333 + -0.5x + x2 = 0

Move the constant term to the right:

Add '6.333333333' to each side of the equation.
-6.333333333 + -0.5x + 6.333333333 + x2 = 0 + 6.333333333

Reorder the terms:
-6.333333333 + 6.333333333 + -0.5x + x2 = 0 + 6.333333333

Combine like terms: -6.333333333 + 6.333333333 = 0.000000000
0.000000000 + -0.5x + x2 = 0 + 6.333333333
-0.5x + x2 = 0 + 6.333333333

Combine like terms: 0 + 6.333333333 = 6.333333333
-0.5x + x2 = 6.333333333

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 6.333333333 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 6.333333333 + 0.0625

Combine like terms: 6.333333333 + 0.0625 = 6.395833333
0.0625 + -0.5x + x2 = 6.395833333

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 6.395833333

Calculate the square root of the right side: 2.528998484

Break this problem into two subproblems by setting 
(x + -0.25) equal to 2.528998484 and -2.528998484.

Subproblem 1

x + -0.25 = 2.528998484 Simplifying x + -0.25 = 2.528998484 Reorder the terms: -0.25 + x = 2.528998484 Solving -0.25 + x = 2.528998484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.528998484 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.528998484 + 0.25 x = 2.528998484 + 0.25 Combine like terms: 2.528998484 + 0.25 = 2.778998484 x = 2.778998484 Simplifying x = 2.778998484

Subproblem 2

x + -0.25 = -2.528998484 Simplifying x + -0.25 = -2.528998484 Reorder the terms: -0.25 + x = -2.528998484 Solving -0.25 + x = -2.528998484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.528998484 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.528998484 + 0.25 x = -2.528998484 + 0.25 Combine like terms: -2.528998484 + 0.25 = -2.278998484 x = -2.278998484 Simplifying x = -2.278998484

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.778998484, -2.278998484}

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